Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

%B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be675 %0 Journal Article %J Extreme Mech. Lett. %D 2019 %T Activation of a muscle as a mapping of stress–strain curves %A Davide Riccobelli %A D. Ambrosi %B Extreme Mech. Lett. %I Elsevier BV %V 28 %P 37–42 %G eng %0 Journal Article %J NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS %D 2018 %T Accelerating the iterative solution of convection-diffusion problems using singular value decomposition %A Giuseppe Pitton %A Luca Heltai %B NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS %P 1–21 %G eng %U https://arxiv.org/abs/1807.09467 %R 10.1002/nla.2211 %0 Journal Article %J Math. Comp. %D 2018 %T Adaptive discontinuous Galerkin methods for elliptic interface problems %A Cangiani, Andrea %A Georgoulis, Emmanuil H. %A Sabawi, Younis A. %B Math. Comp. %V 87 %P 2675–2707 %G eng %U https://doi.org/10.1090/mcom/3322 %R 10.1090/mcom/3322 %0 Journal Article %J SIAM Journal on Applied Mathematics %D 2018 %T Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness %A Giuliano Lazzaroni %A Lorenzo Nardini %XWe analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

%B SIAM Journal on Applied Mathematics %V 78 %P 1206-1227 %G eng %U https://doi.org/10.1137/17M1147354 %R 10.1137/17M1147354 %0 Journal Article %J JOURNAL OF INDUSTRIAL TEXTILES %D 2018 %T An authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production %A Rafiei, S. %A Noroozi, B. %A Luca Heltai %A Haghi, A. K. %B JOURNAL OF INDUSTRIAL TEXTILES %V 47 %P 1791–1811 %G eng %R 10.1177/1528083717710711 %0 Journal Article %J Communication in Applied Industrial Mathematics %D 2017 %T Advances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method %A Giovanni Stabile %A Saddam Hijazi %A Stefano Lorenzi %A Andrea Mola %A Gianluigi Rozza %K finite volume, CFD %K Reduced order methods %XVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

%B Communication in Applied Industrial Mathematics %G eng %U https://arxiv.org/abs/1701.03424 %9 reviewed %0 Report %D 2017 %T Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions %A Massimiliano Berti %A Jean-Marc Delort %X The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions. %G en %U http://preprints.sissa.it/handle/1963/35285 %1 35590 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-05-30T09:17:49Z No. of bitstreams: 1 1702.04674.pdf: 2311619 bytes, checksum: 0765035340f77780899e30e93390092b (MD5) %0 Journal Article %J Random Matrices: Theory and Applications %D 2017 %T Analytic geometry of semisimple coalescent Frobenius structures %A Giordano Cotti %A Davide Guzzetti %XWe present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop “Asymptotic and Computational Aspects of Complex Differential Equations” at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians.

%B Random Matrices: Theory and Applications %V 06 %P 1740004 %G eng %U https://doi.org/10.1142/S2010326317400044 %R 10.1142/S2010326317400044 %0 Journal Article %J Topol. Methods Nonlinear Anal. %D 2017 %T An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators %A Guglielmo Feltrin %A Fabio Zanolin %B Topol. Methods Nonlinear Anal. %I Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies %V 50 %P 683–726 %G eng %U https://doi.org/10.12775/TMNA.2017.038 %R 10.12775/TMNA.2017.038 %0 Journal Article %J Journal of Scientific Computing %D 2017 %T On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics %A Giuseppe Pitton %A Gianluigi Rozza %XIn this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

%B Journal of Scientific Computing %G eng %R 10.1007/s10915-017-0419-6 %0 Journal Article %J Journal of Differential Equations %D 2017 %T An avoiding cones condition for the Poincaré–Birkhoff Theorem %A Alessandro Fonda %A Paolo Gidoni %K Avoiding cones condition %K Hamiltonian systems %K Periodic solutions %K Poincaré–Birkhoff theorem %XWe provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincaré–Birkhoff fixed point Theorem for Poincaré maps of Hamiltonian systems.

%B Journal of Differential Equations %V 262 %P 1064 - 1084 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616303278 %R https://doi.org/10.1016/j.jde.2016.10.002 %0 Journal Article %J SIAM J. Sci. Comput. %D 2016 %T Adaptivity and blow-up detection for nonlinear evolution problems %A Cangiani, Andrea %A Georgoulis, Emmanuil H. %A Kyza, Irene %A Metcalfe, Stephen %B SIAM J. Sci. Comput. %V 38 %P A3833–A3856 %G eng %U https://doi.org/10.1137/16M106073X %R 10.1137/16M106073X %0 Conference Paper %B Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, %D 2016 %T Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives %A Filippo Salmoiraghi %A Francesco Ballarin %A Giovanni Corsi %A Andrea Mola %A Marco Tezzele %A Gianluigi Rozza %E Papadrakakis, M. %E Papadopoulos, V. %E Stefanou, G. %E Plevris, V. %XSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

%B Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, %I ECCOMAS %C Crete, Greece %8 06/2016 %G en %1 35466 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-13T00:28:01Z No. of bitstreams: 1 eccomas2016_AROMA.pdf: 1846196 bytes, checksum: 9636e713df80de178d87fd2feff76f91 (MD5) %0 Journal Article %J ESAIM: COCV %D 2016 %T On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity %A Giovanni Bellettini %A Lucia Tealdi %A Maurizio Paolini %K Area functional %XIn this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

%B ESAIM: COCV %V 22 %P 29-63 %G en %U https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html %N 1 %1 7257 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2013-11-29T13:51:49Z No. of bitstreams: 1 bellettini_paolini_tealdi_SISSAprprint.pdf: 705021 bytes, checksum: 98a550aeb5925de05f6b419569ccd283 (MD5) %R 10.1051/cocv/2014065 %0 Journal Article %J SIGMA Symmetry Integrability Geom. Methods Appl. %D 2016 %T On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight %A Marco Bertola %A Alexander Tovbis %B SIGMA Symmetry Integrability Geom. Methods Appl. %V 12 %P Paper No. 118, 50 pages %G eng %U http://dx.doi.org/10.3842/SIGMA.2016.118 %R 10.3842/SIGMA.2016.118 %0 Journal Article %D 2015 %T Anisotropic mean curvature on facets and relations with capillarity %A Stefano Amato %A Lucia Tealdi %A Giovanni Bellettini %XWe discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

%I de Gruyter %G en_US %U http://urania.sissa.it/xmlui/handle/1963/34481 %1 34663 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Stefano Amato (samato@sissa.it) on 2015-08-06T08:33:21Z No. of bitstreams: 1 amato_bellettini_tealdi.pdf: 561517 bytes, checksum: ee2370b8b8ae04078e1e8eae84d37bdd (MD5) %R 10.1515/geofl-2015-0005 %0 Journal Article %J Constr. Approx. %D 2015 %T Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation %A Marco Bertola %A Alexander Tovbis %B Constr. Approx. %V 41 %P 529–587 %G eng %U http://dx.doi.org/10.1007/s00365-015-9288-0 %R 10.1007/s00365-015-9288-0 %0 Journal Article %D 2014 %T An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds %A Massimiliano Berti %A Livia Corsi %A Michela Procesi %X We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34651 %1 34858 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:19:54Z No. of bitstreams: 1 preprint2014.pdf: 549502 bytes, checksum: 4896c2df9fba6a09abb33941adb07837 (MD5) %R 10.1007/s00220-014-2128-4 %0 Journal Article %D 2014 %T Achieving unanimous opinions in signed social networks %A Claudio Altafini %A Gabriele Lini %X Being able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n. %I Institute of Electrical and Electronics Engineers Inc. %G en %U http://urania.sissa.it/xmlui/handle/1963/34935 %1 35137 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-06T12:24:07Z (GMT) No. of bitstreams: 0 %R 10.1109/ECC.2014.6862161 %0 Journal Article %J IMA J. Numer. Anal. %D 2014 %T Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems %A Cangiani, Andrea %A Georgoulis, Emmanuil H. %A Metcalfe, Stephen %B IMA J. Numer. Anal. %V 34 %P 1578–1597 %G eng %U https://doi.org/10.1093/imanum/drt052 %R 10.1093/imanum/drt052 %0 Journal Article %D 2014 %T Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy. %I SISSA %G eng %U http://hdl.handle.net/1963/7242 %0 Journal Article %D 2014 %T Approximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %X We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34645 %1 34849 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T16:50:03Z No. of bitstreams: 1 preprint2014.pdf: 191569 bytes, checksum: 33ef336bcd23cb79195af6fc13704f62 (MD5) %R 10.1007/s10455-014-9433-1 %0 Journal Article %D 2014 %T Approximate Hitchin-Kobayashi correspondence for Higgs G-bundles %A Ugo Bruzzo %A Beatriz Graña Otero %X We announce a result about the extension of the Hitchin-Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact Kähler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure. %I World Scientific Publishing %G en %U http://urania.sissa.it/xmlui/handle/1963/35095 %1 35350 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-02T12:29:37Z (GMT) No. of bitstreams: 0 %R 10.1142/S0219887814600159 %0 Report %D 2013 %T Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity %A Matteo Focardi %A Flaviana Iurlano %K Functions of bounded deformation %XWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

%I SISSA %G en %U http://hdl.handle.net/1963/6615 %1 6573 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Flaviana Iurlano (iurlano@sissa.it) on 2013-05-13T11:26:04Z No. of bitstreams: 1 coesivo17_preprint_SISSA.pdf: 482275 bytes, checksum: 890efd398f9ff18a36d5b18fc90f8107 (MD5) %0 Journal Article %D 2013 %T Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K singular nonlinear parabolic equations, Hilbert transform, thin films %X In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6]. %I Springer %G en %U http://hdl.handle.net/1963/7245 %1 7284 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-01-15T08:47:14Z No. of bitstreams: 1 DM-Fon-Leo.pdf: 409459 bytes, checksum: 07429e936667a481a2c093217e585e84 (MD5) %R 10.1007/s00205-014-0730-4 %0 Thesis %D 2013 %T An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems %A Flaviana Iurlano %K Functions of bounded deformation %I SISSA %G en %1 7203 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Flaviana Iurlano (iurlano@sissa.it) on 2013-10-23T12:46:25Z No. of bitstreams: 1 Iurlano - PhD Thesis.pdf: 1234569 bytes, checksum: e031f9fd97f6a1662f96f1caf2bc564e (MD5) %0 Journal Article %D 2013 %T Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length %A Paolo Tilli %A Davide Zucco %X We consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian. %I Society for Industrial and Applied Mathematics %G en %U http://urania.sissa.it/xmlui/handle/1963/35141 %1 35379 %2 Physics %4 1 %# MAT/05 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-09T16:12:39Z (GMT) No. of bitstreams: 0 %R 10.1137/130916825 %0 Report %D 2013 %T Attainment results for nematic elastomers %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %X We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. %I SISSA %G en %U http://hdl.handle.net/1963/7174 %1 7201 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-10-22T14:32:26Z No. of bitstreams: 1 Ago-DM-DeS-13-sissa.pdf: 394672 bytes, checksum: d02690a6c7f206310d28d253ce53d0d3 (MD5) %0 Journal Article %J Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %D 2012 %T Asymptotics of the s-perimeter as s →0 %A Serena Dipierro %A Alessio Figalli %A Giampiero Palatucci %A Enrico Valdinoci %XWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

%B Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %I American Institute of Mathematical Sciences %G en %1 7317 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T15:55:21Z No. of bitstreams: 1 1204.0750v2.pdf: 216883 bytes, checksum: 3ee8d497a2c0f9a211ec5327e8aa6b9a (MD5) %R 10.3934/dcds.2013.33.2777 %0 Journal Article %J IET systems biology. 2011 Jul; 5(4):269-79 %D 2011 %T Adaptation as a genome-wide autoregulatory principle in the stress response of yeast. %A F Eduati %A B Di Camillo %A G Toffolo %A Claudio Altafini %A Giovanna De Palo %A Mattia Zampieri %X The gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products. %B IET systems biology. 2011 Jul; 5(4):269-79 %I The Institution of Engineering and Technology %G en %U http://hdl.handle.net/1963/5106 %1 4922 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-25T13:05:49Z\\r\\nNo. of bitstreams: 1\\r\\nDePaEdal10.pdf: 2390366 bytes, checksum: f6550b1052efeb53942e47cae9632899 (MD5) %R 10.1049/iet-syb.2009.0050 %0 Journal Article %J J.Phys.A: Math.Theor. 44 (2011) 215203 %D 2011 %T An asymptotic reduction of a Painlevé VI equation to a Painlevé III %A Davide Guzzetti %X When the independent variable is close to a critical point, it is shown that\\r\\nPVI can be asymptotically reduced to PIII. In this way, it is possible to\\r\\ncompute the leading term of the critical behaviors of PVI transcendents\\r\\nstarting from the behaviors of PIII transcendents. %B J.Phys.A: Math.Theor. 44 (2011) 215203 %I IOP Publishing %G en %U http://hdl.handle.net/1963/5124 %1 4940 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-28T15:06:23Z\\nNo. of bitstreams: 1\\n1101.4705v1.pdf: 150593 bytes, checksum: 32af4569fb34ae6257486f096be0142b (MD5) %R 10.1088/1751-8113/44/21/215203 %0 Journal Article %J Proc. Amer. Math. Soc. 139 (2011), 1023-1032 %D 2011 %T Axial symmetry of some steady state solutions to nonlinear Schrödinger equations %A Changfeng Gui %A Andrea Malchiodi %A Haoyuan Xu %A Paul Yang %K Nonlinear Schrödinger equation %X In this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space. %B Proc. Amer. Math. Soc. 139 (2011), 1023-1032 %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/4100 %1 304 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-10T10:42:02Z\\r\\nNo. of bitstreams: 1\\r\\nGui_Malchiodi_75M.pdf: 196044 bytes, checksum: ed4d2f1be79209d4b3e7d428564d043a (MD5) %R 10.1090/S0002-9939-2010-10638-X %0 Journal Article %J Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis %D 2010 %T An abstract Nash-Moser theorem with parameters and applications to PDEs %A Massimiliano Berti %A Philippe Bolle %A Michela Procesi %K Abstracting %K Aircraft engines %K Finite dimensional %K Hamiltonian PDEs %K Implicit function theorem %K Invariant tori %K Iterative schemes %K Linearized operators %K Mathematical operators %K Moser theorem %K Non-Linearity %K Nonlinear equations %K Nonlinear wave equation %K Periodic solution %K Point of interest %K Resonance phenomena %K Small divisors %K Sobolev %K Wave equations %X We prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. © 2009 Elsevier Masson SAS. All rights reserved. %B Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis %V 27 %P 377-399 %G eng %R 10.1016/j.anihpc.2009.11.010 %0 Thesis %D 2010 %T Almost-Riemannian Geometry from a Control Theoretical Viewpoint %A Roberta Ghezzi %I SISSA %G en %U http://hdl.handle.net/1963/4705 %1 4482 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Davide Barilari (barilari@sissa.it) on 2011-10-13T08:13:37Z\\r\\nNo. of bitstreams: 1\\r\\nghezzi-PhD-thesis.pdf: 870834 bytes, checksum: 868d097fff7d3a6646b2bacc98dfeb4b (MD5) %0 Conference Proceedings %B PoS CNCFG2010:027,2010 %D 2010 %T Aspects of Quantum Field Theory on Quantum Spacetime %A Gherardo Piacitelli %X We provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation. %B PoS CNCFG2010:027,2010 %I SISSA %G en %U http://hdl.handle.net/1963/4171 %1 3893 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-20T14:32:21Z\\nNo. of bitstreams: 1\\n1103.3405v1.pdf: 305413 bytes, checksum: 094028cf6f36b4949d9db8c681bf4cec (MD5) %0 Journal Article %J Journal of Differential Equations %D 2008 %T Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields %A Alessandro Selvitella %XIn this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

%B Journal of Differential Equations %V 245 %P 2566 - 2584 %G eng %U http://www.sciencedirect.com/science/article/pii/S002203960800243X %R https://doi.org/10.1016/j.jde.2008.05.012 %0 Journal Article %J Comm. Pure Appl. Math. 60 (2007) 1559-1622 %D 2007 %T Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy %A Stefano Bianchini %A Bernard Hanouzet %A Roberto Natalini %X We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition. %B Comm. Pure Appl. Math. 60 (2007) 1559-1622 %G en_US %U http://hdl.handle.net/1963/1780 %1 2764 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T10:33:17Z\\nNo. of bitstreams: 1\\n83M.pdf: 393359 bytes, checksum: f3f7b61564332b98b8706af95942dd69 (MD5) %R 10.1002/cpa.20195 %0 Journal Article %J Ann. Henri Poincar´e 8 (2007), 301–336 %D 2007 %T The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics %A Davide Guzzetti %A Giorgio Mantica %X We study measures generated by systems of linear iterated functions,\r\ntheir Fourier transforms, and those of their orthogonal polynomials. We\r\ncharacterize the asymptotic behaviours of their discrete and continuous averages.\r\nFurther related quantities are analyzed, and relevance of this analysis\r\nto quantum mechanics is briefly discussed %B Ann. Henri Poincar´e 8 (2007), 301–336 %I 2007 Birkh¨auser Verlag Basel/Switzerland %G en %1 6480 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:11:23Z\nNo. of bitstreams: 1\n11-GuzMantica07.pdf: 924495 bytes, checksum: 5897cbac3fb5b378b02bf5cdae1273ea (MD5) %R 10.1007/s00023-006-0309-1 %0 Journal Article %J Arch. Ration. Mech. Anal. 183 (2007) 163-185 %D 2007 %T Asymptotic variational wave equations %A Alberto Bressan %A Zhang Ping %A Zheng Yuxi %X We investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data. %B Arch. Ration. Mech. Anal. 183 (2007) 163-185 %G en_US %U http://hdl.handle.net/1963/2182 %1 2062 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T07:08:27Z\\nNo. of bitstreams: 1\\n0502124v1.pdf: 205978 bytes, checksum: a1efb4667d7315509947b4d7a4999bd1 (MD5) %R 10.1007/s00205-006-0014-8 %0 Report %D 2006 %T Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics %A Claudio Altafini %A Francesco Ticozzi %X We propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process. %G en_US %U http://hdl.handle.net/1963/1727 %1 2424 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-30T12:56:41Z\\nNo. of bitstreams: 1\\nquant-ph0510222.pdf: 574764 bytes, checksum: d53ebd4e4afe123a6476bed544c4b9df (MD5) %0 Report %D 2006 %T An artificial viscosity approach to quasistatic crack growth %A Rodica Toader %A Chiara Zanini %X We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero. %G en_US %U http://hdl.handle.net/1963/1850 %1 2367 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-26T10:13:38Z\\nNo. of bitstreams: 1\\nmath.AP-0607596.pdf: 297980 bytes, checksum: 7a13d5d5fe36a4577923b3ccd0b0acaf (MD5) %0 Journal Article %J Comm. Anal. Geom. 13 (2005) 187-252 %D 2005 %T Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$ %A Sagun Chanillo %A Andrea Malchiodi %X Given a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron. %B Comm. Anal. Geom. 13 (2005) 187-252 %I International Press %G en_US %U http://hdl.handle.net/1963/3533 %1 731 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T10:28:24Z\\nNo. of bitstreams: 1\\n0205106v1.pdf: 508637 bytes, checksum: 9894eb1ef04ac61cd02aebdee04ff5fa (MD5) %0 Journal Article %J SIAM J. Control Optim. 43 (2005) 2166-2190 %D 2005 %T On the attainable set for Temple class systems with boundary controls %A Fabio Ancona %A Giuseppe Maria Coclite %X Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology. %B SIAM J. Control Optim. 43 (2005) 2166-2190 %I SISSA Library %G en %U http://hdl.handle.net/1963/1581 %1 2537 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:51Z (GMT). No. of bitstreams: 1\\nmath.AP0205167.pdf: 356214 bytes, checksum: 05474bd7744107031887816262b561b3 (MD5)\\n Previous issue date: 2002 %R 10.1137/S0363012902407776 %0 Journal Article %J Amer. Math. Soc. Transl. 212 (2004)\\n75-132. %D 2004 %T On almost duality for Frobenius manifolds %A Boris Dubrovin %X We present a universal construction of almost duality for Frobenius manifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by examples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg - Witten duality. %B Amer. Math. Soc. Transl. 212 (2004)\\n75-132. %G en_US %U http://hdl.handle.net/1963/2543 %1 1576 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:40:01Z\\nNo. of bitstreams: 1\\n0307374v2.pdf: 617411 bytes, checksum: 7c8c52a06ea53850475a3e7055ce9af1 (MD5) %0 Journal Article %J Astérisque. Issue 297, 2004, Pages 35-65 %D 2004 %T On analytic families of invariant tori for PDEs %A Boris Dubrovin %X We propose to apply a version of the classical Stokes\\r\\nexpansion method to the perturbative construction of invariant tori for\\r\\nPDEs corresponding to solutions quasiperiodic in space and time variables.\\r\\nWe argue that, for integrable PDEs all but finite number of the\\r\\nsmall divisors arising in the perturbative analysis cancel. As an illustrative\\r\\nexample we establish such cancellations for the case of KP equation.\\r\\nIt is proved that, under mild assumptions about decay of the magnitude\\r\\nof the Fourier modes all analytic families of finite-dimensional invariant\\r\\ntori for KP are given by the Krichever construction in terms of thetafunctions\\r\\nof Riemann surfaces. We also present an explicit construction\\r\\nof infinite dimensional real theta-functions and corresponding quasiperiodic\\r\\nsolutions to KP as sums of infinite number of interacting plane\\r\\nwaves. %B Astérisque. Issue 297, 2004, Pages 35-65 %I SISSA %G en %U http://hdl.handle.net/1963/6474 %1 6420 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:58:35Z\\nNo. of bitstreams: 1\\ndubrovin_2004_asterisque.pdf: 318797 bytes, checksum: 3fe6968166d8ac662d44abd508bde574 (MD5) %0 Journal Article %J Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %D 2004 %T Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains %A Gianni Dal Maso %A Francois Murat %X We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains. %B Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %I SISSA Library %G en %U http://hdl.handle.net/1963/1611 %1 2507 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:17Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0205225.pdf: 404809 bytes, checksum: 472524cb28afed2e55fcf0a7c46e7598 (MD5)\\r\\n Previous issue date: 2002 %0 Journal Article %J Applied Math.Optim. 48 (2003), no.1, p.39-66 %D 2003 %T Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations %A Gianni Dal Maso %A Helene Frankowska %B Applied Math.Optim. 48 (2003), no.1, p.39-66 %I SISSA Library %G en %U http://hdl.handle.net/1963/1625 %1 2493 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:30Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207230.pdf: 302400 bytes, checksum: e660ec855386e1a29edd2e20f7abc796 (MD5)\\r\\n Previous issue date: 2002 %R 10.1007/s00245-003-0768-4 %0 Journal Article %J J. Differ. Equations, 2002, 180, 395 %D 2002 %T Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type %A Jean-Marc Mercier %A Benedetto Piccoli %B J. Differ. Equations, 2002, 180, 395 %I SISSA Library %G en %U http://hdl.handle.net/1963/1491 %1 2672 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:09Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1006/jdeq.2001.4066 %0 Journal Article %J Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 43, Part 1, 2, Natsīonal. Akad. Nauk Ukraïni, Īnst. Mat., Kiev, 2002 %D 2002 %T Arnold diffusion: a functional analysis approach %A Massimiliano Berti %X We present, in the context of nearly integrable Hamiltonian systems, a functional analysis approach to study the “splitting of the whiskers” and the “shadowing problem” developed in collaboration with P. Bolle in the recent papers [1] and [2] . This method is applied to the problem of Arnold diffusion for nearly integrable partially isochronous systems improving known results. %B Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 43, Part 1, 2, Natsīonal. Akad. Nauk Ukraïni, Īnst. Mat., Kiev, 2002 %I Natsīonal. Akad. Nauk Ukraïni %G en %1 7269 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-12-09T08:37:48Z No. of bitstreams: 1 Berti712-719.pdf: 135161 bytes, checksum: 75afb14b28171db9cab374b3ccbbc265 (MD5) %0 Journal Article %J Asymptotic Anal., 2001, 25, 149-181 %D 2001 %T Adiabatic limits of closed orbits for some Newtonian systems in R-n %A Andrea Malchiodi %X We deal with a Newtonian system like x\\\'\\\' + V\\\'(x) = 0. We suppose that V: \\\\R^n \\\\to \\\\R possesses an (n-1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M. %B Asymptotic Anal., 2001, 25, 149-181 %I SISSA Library %G en %U http://hdl.handle.net/1963/1511 %1 2652 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:25Z (GMT). No. of bitstreams: 1\\nmath.DS0006229.pdf: 332070 bytes, checksum: 05767d978ee641c261858a4e235cfeb3 (MD5)\\n Previous issue date: 2000 %0 Journal Article %D 2000 %T Abnormal extremals for minimum time on the plane %A Ugo Boscain %A Benedetto Piccoli %I SISSA Library %G en %U http://hdl.handle.net/1963/1508 %1 2655 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:23Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Journal Article %D 2000 %T Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems %A Massimiliano Berti %A Philippe Bolle %I SISSA Library %G en %U http://hdl.handle.net/1963/1554 %1 2564 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:03Z (GMT). No. of bitstreams: 1\\nmath.DS0011017.pdf: 394514 bytes, checksum: 1c7ce3b0641b2ada647963d5a00697e0 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Lett. Math. Phys., 2000, 52, 339 %D 2000 %T A(SLq(2)) at roots of unity is a free module over A(SL(2)) %A Ludwik Dabrowski %A Cesare Reina %A Alessandro Zampa %B Lett. Math. Phys., 2000, 52, 339 %I SISSA Library %G en %U http://hdl.handle.net/1963/1500 %1 2663 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:03:17Z (GMT). No. of bitstreams: 1\\nmath.QA0004092.pdf: 71107 bytes, checksum: ad69901d378f79db9f98cc05c5caabb4 (MD5)\\n Previous issue date: 2000 %R 10.1023/A:1007601131002 %0 Journal Article %J Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 %D 1999 %T The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional %A Matteo Negri %X We compute explicitly the anisotropy effect in the H1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations. %B Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 %I Taylor and Francis %G en %U http://hdl.handle.net/1963/1276 %1 3179 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1080/01630569908816934 %0 Thesis %D 1999 %T Approximation, Stability and control for Conservation Laws %A Andrea Marson %I SISSA %G en %U http://hdl.handle.net/1963/5500 %1 5331 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-02-15T08:31:14Z\\nNo. of bitstreams: 1\\nPhD_Marson_Andrea.pdf: 6489276 bytes, checksum: 5c9f28283a0b07370b455c460bcb2ea7 (MD5) %0 Journal Article %J Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %D 1999 %T Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %@ 1618-1891 %G en %U http://hdl.handle.net/1963/6433 %1 6374 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:25:49Z\\nNo. of bitstreams: 0 %R 10.1007/BF01759365 %0 Thesis %D 1998 %T Algebraic Solutions to the Painlevé-VI Equation and Reflection Groups %A Marta Mazzocco %K Painlevé VI equation %I SISSA %G en %U http://hdl.handle.net/1963/5574 %1 5402 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-03-07T08:50:25Z\\nNo. of bitstreams: 1\\nPhD_Mazzocco_Marta.pdf: 10633506 bytes, checksum: 7f215e60776f5f60539fc4f7ce22abd0 (MD5) %0 Journal Article %J Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %D 1998 %T Asymptotic behavior of nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %I SISSA Library %G en %U http://hdl.handle.net/1963/1064 %1 2738 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Report %D 1994 %T Algebraic-geometrical Darboux coordinates in R-matrix formalism %A P. Diener %A Boris Dubrovin %I SISSA %G en_US %U http://hdl.handle.net/1963/3655 %1 650 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-19T09:50:48Z\\nNo. of bitstreams: 1\\nconvert_SCAN-9409240.pdf: 910778 bytes, checksum: 4c51b62625fe5debfdaa55aa2db61ff8 (MD5) %0 Thesis %D 1994 %T Analysis of Singularity Structures for Quasi-Integrable Hamiltonian Systems %A Simonetta Abenda %K Hamiltonian systems %I SISSA %G en %U http://hdl.handle.net/1963/5685 %1 5534 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-04-12T08:01:54Z\\nNo. of bitstreams: 1\\nPhD_Abenda_Simonetta.pdf: 8414314 bytes, checksum: b540a9a3c486080792ac8700cb9c1d79 (MD5) %0 Thesis %D 1994 %T Asymptotic Behaviour of Dirichlet Problems in Perforated Domains %A Adriana Garroni %K Dirichlet problems %I SISSA %G en %U http://hdl.handle.net/1963/5714 %1 5566 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-04-16T10:54:30Z\\nNo. of bitstreams: 1\\nPhD_Garroni_Adriana.pdf: 8799112 bytes, checksum: 71df771317b5fd6f6add4ee83805d0e5 (MD5) %0 Journal Article %J Nuclear Phys. B. Proc. Suppl. 18A (1990), 171 %D 1990 %T Algebraic differential calculus for gauge theories %A Giovanni Landi %A Giuseppe Marmo %B Nuclear Phys. B. Proc. Suppl. 18A (1990), 171 %I SISSA Library %G en %U http://hdl.handle.net/1963/891 %1 2900 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:39:14Z (GMT). No. of bitstreams: 1\\n135_89.pdf: 1275996 bytes, checksum: 206cd5e78d64c8a5f30cb85a3329b5cd (MD5)\\n Previous issue date: 1989 %R 10.1016/0920-5632(90)90649-F %0 Journal Article %J Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %D 1989 %T An approach to the thin obstacle problem for variational functionals depending on vector %A Gianni Dal Maso %A Roberta Musina %B Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %I SISSA Library %G en %U http://hdl.handle.net/1963/802 %1 2989 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:08Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Phys. Lett. B 201 (1988), no. 1, 101-104. %D 1988 %T Algebraic reduction of the \\\'t Hooft-Polyakov monopole to the Dirac monopole. %A Giovanni Landi %A Giuseppe Marmo %B Phys. Lett. B 201 (1988), no. 1, 101-104. %I SISSA Library %G en %U http://hdl.handle.net/1963/578 %1 3326 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:34:36Z (GMT). No. of bitstreams: 1\\n97_87.pdf: 211964 bytes, checksum: 4b695a8c6442b33d501e9d46b8d1f65d (MD5)\\n Previous issue date: 1987 %R 10.1016/0370-2693(88)90088-3 %0 Thesis %D 1988 %T An Algebraic Setting for Gauge Theories %A Giovanni Landi %I SISSA %G en %U http://hdl.handle.net/1963/5828 %1 5677 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-10T11:47:30Z\\nNo. of bitstreams: 1\\nPhD_Landi_Giovanni.pdf: 12850619 bytes, checksum: f875567d94d0cea44fd8c704db2b3222 (MD5) %0 Journal Article %D 1983 %T On the asymptotic behaviour of solutions to Pazy\\\'s class of evolution equations %A Giovanni Vidossich %I SISSA Library %G en %U http://hdl.handle.net/1963/276 %1 3691 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:27:33Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1983