We 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.

VL - 78 UR - https://doi.org/10.1137/17M1147354 ER - TY - JOUR T1 - An authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production JF - JOURNAL OF INDUSTRIAL TEXTILES Y1 - 2018 A1 - Rafiei, S. A1 - Noroozi, B. A1 - Luca Heltai A1 - Haghi, A. K. VL - 47 ER - TY - JOUR T1 - Advances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method JF - Communication in Applied Industrial Mathematics Y1 - 2017 A1 - Giovanni Stabile A1 - Saddam Hijazi A1 - Stefano Lorenzi A1 - Andrea Mola A1 - Gianluigi Rozza KW - finite volume, CFD KW - Reduced order methods AB -Vortex 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.

UR - https://arxiv.org/abs/1701.03424 ER - TY - RPRT T1 - Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions Y1 - 2017 A1 - Massimiliano Berti A1 - Jean-Marc Delort AB - 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. UR - http://preprints.sissa.it/handle/1963/35285 U1 - 35590 U2 - Mathematics ER - TY - JOUR T1 - Analytic geometry of semisimple coalescent Frobenius structures JF - Random Matrices: Theory and Applications Y1 - 2017 A1 - Giordano Cotti A1 - Davide Guzzetti AB -We 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.

VL - 06 UR - https://doi.org/10.1142/S2010326317400044 ER - TY - JOUR T1 - An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators JF - Topol. Methods Nonlinear Anal. Y1 - 2017 A1 - Guglielmo Feltrin A1 - Fabio Zanolin PB - Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies VL - 50 UR - https://doi.org/10.12775/TMNA.2017.038 ER - TY - JOUR T1 - On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics JF - Journal of Scientific Computing Y1 - 2017 A1 - Giuseppe Pitton A1 - Gianluigi Rozza AB -In 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.

ER - TY - JOUR T1 - An avoiding cones condition for the Poincaré–Birkhoff Theorem JF - Journal of Differential Equations Y1 - 2017 A1 - Alessandro Fonda A1 - Paolo Gidoni KW - Avoiding cones condition KW - Hamiltonian systems KW - Periodic solutions KW - Poincaré–Birkhoff theorem AB -We 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.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039616303278 ER - TY - CONF T1 - Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives T2 - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, Y1 - 2016 A1 - Filippo Salmoiraghi A1 - Francesco Ballarin A1 - Giovanni Corsi A1 - Andrea Mola A1 - Marco Tezzele A1 - Gianluigi Rozza ED - Papadrakakis, M. ED - Papadopoulos, V. ED - Stefanou, G. ED - Plevris, V. AB -Several 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.

JF - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, PB - ECCOMAS CY - Crete, Greece U1 - 35466 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity JF - ESAIM: COCV Y1 - 2016 A1 - Giovanni Bellettini A1 - Lucia Tealdi A1 - Maurizio Paolini KW - Area functional AB -In 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.

VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html IS - 1 U1 - 7257 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight JF - SIGMA Symmetry Integrability Geom. Methods Appl. Y1 - 2016 A1 - Marco Bertola A1 - Alexander Tovbis VL - 12 UR - http://dx.doi.org/10.3842/SIGMA.2016.118 ER - TY - JOUR T1 - Anisotropic mean curvature on facets and relations with capillarity Y1 - 2015 A1 - Stefano Amato A1 - Lucia Tealdi A1 - Giovanni Bellettini AB -We 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.

PB - de Gruyter UR - http://urania.sissa.it/xmlui/handle/1963/34481 U1 - 34663 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation JF - Constr. Approx. Y1 - 2015 A1 - Marco Bertola A1 - Alexander Tovbis VL - 41 UR - http://dx.doi.org/10.1007/s00365-015-9288-0 ER - TY - JOUR T1 - An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds Y1 - 2014 A1 - Massimiliano Berti A1 - Livia Corsi A1 - Michela Procesi AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34651 U1 - 34858 U2 - Mathematics ER - TY - JOUR T1 - Achieving unanimous opinions in signed social networks Y1 - 2014 A1 - Claudio Altafini A1 - Gabriele Lini AB - 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. PB - Institute of Electrical and Electronics Engineers Inc. UR - http://urania.sissa.it/xmlui/handle/1963/34935 U1 - 35137 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7242 N1 - 45 pages ER - TY - JOUR T1 - Approximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles Y1 - 2014 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34645 U1 - 34849 U2 - Mathematics ER - TY - JOUR T1 - Approximate Hitchin-Kobayashi correspondence for Higgs G-bundles Y1 - 2014 A1 - Ugo Bruzzo A1 - Beatriz Graña Otero AB - 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. PB - World Scientific Publishing UR - http://urania.sissa.it/xmlui/handle/1963/35095 U1 - 35350 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity Y1 - 2013 A1 - Matteo Focardi A1 - Flaviana Iurlano KW - Functions of bounded deformation AB -We 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 $\gamma>0$.

PB - SISSA UR - http://hdl.handle.net/1963/6615 U1 - 6573 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces Y1 - 2013 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni KW - singular nonlinear parabolic equations, Hilbert transform, thin films AB - 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]. PB - Springer UR - http://hdl.handle.net/1963/7245 U1 - 7284 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems Y1 - 2013 A1 - Flaviana Iurlano KW - Functions of bounded deformation PB - SISSA U1 - 7203 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length Y1 - 2013 A1 - Paolo Tilli A1 - Davide Zucco AB - 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. PB - Society for Industrial and Applied Mathematics UR - http://urania.sissa.it/xmlui/handle/1963/35141 U1 - 35379 U2 - Physics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Attainment results for nematic elastomers Y1 - 2013 A1 - Virginia Agostiniani A1 - Gianni Dal Maso A1 - Antonio DeSimone AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7174 U1 - 7201 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Asymptotics of the s-perimeter as s →0 JF - Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 Y1 - 2012 A1 - Serena Dipierro A1 - Alessio Figalli A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -We 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.

PB - American Institute of Mathematical Sciences U1 - 7317 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Adaptation as a genome-wide autoregulatory principle in the stress response of yeast. JF - IET systems biology. 2011 Jul; 5(4):269-79 Y1 - 2011 A1 - F Eduati A1 - B Di Camillo A1 - G Toffolo A1 - Claudio Altafini A1 - Giovanna De Palo A1 - Mattia Zampieri AB - 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. PB - The Institution of Engineering and Technology UR - http://hdl.handle.net/1963/5106 U1 - 4922 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An asymptotic reduction of a Painlevé VI equation to a Painlevé III JF - J.Phys.A: Math.Theor. 44 (2011) 215203 Y1 - 2011 A1 - Davide Guzzetti AB - 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/5124 U1 - 4940 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Axial symmetry of some steady state solutions to nonlinear Schrödinger equations JF - Proc. Amer. Math. Soc. 139 (2011), 1023-1032 Y1 - 2011 A1 - Changfeng Gui A1 - Andrea Malchiodi A1 - Haoyuan Xu A1 - Paul Yang KW - Nonlinear Schrödinger equation AB - 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. PB - American Mathematical Society UR - http://hdl.handle.net/1963/4100 U1 - 304 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An abstract Nash-Moser theorem with parameters and applications to PDEs JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis Y1 - 2010 A1 - Massimiliano Berti A1 - Philippe Bolle A1 - Michela Procesi KW - Abstracting KW - Aircraft engines KW - Finite dimensional KW - Hamiltonian PDEs KW - Implicit function theorem KW - Invariant tori KW - Iterative schemes KW - Linearized operators KW - Mathematical operators KW - Moser theorem KW - Non-Linearity KW - Nonlinear equations KW - Nonlinear wave equation KW - Periodic solution KW - Point of interest KW - Resonance phenomena KW - Small divisors KW - Sobolev KW - Wave equations AB - 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. VL - 27 N1 - cited By (since 1996)9 ER - TY - THES T1 - Almost-Riemannian Geometry from a Control Theoretical Viewpoint Y1 - 2010 A1 - Roberta Ghezzi PB - SISSA UR - http://hdl.handle.net/1963/4705 U1 - 4482 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - Generic T1 - Aspects of Quantum Field Theory on Quantum Spacetime T2 - PoS CNCFG2010:027,2010 Y1 - 2010 A1 - Gherardo Piacitelli AB - 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. JF - PoS CNCFG2010:027,2010 PB - SISSA UR - http://hdl.handle.net/1963/4171 N1 - 25 pages, active hyperlinks. Corfu Summer Institute on Elementary\\r\\n Particles and Physics - Workshop on Non Commutative Field Theory and Gravity,\\r\\n September 8-12, 2010, Corfu Greece U1 - 3893 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields JF - Journal of Differential Equations Y1 - 2008 A1 - Alessandro Selvitella AB -In 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.

VL - 245 UR - http://www.sciencedirect.com/science/article/pii/S002203960800243X ER - TY - JOUR T1 - Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy JF - Comm. Pure Appl. Math. 60 (2007) 1559-1622 Y1 - 2007 A1 - Stefano Bianchini A1 - Bernard Hanouzet A1 - Roberto Natalini AB - 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. UR - http://hdl.handle.net/1963/1780 U1 - 2764 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics JF - Ann. Henri Poincar´e 8 (2007), 301–336 Y1 - 2007 A1 - Davide Guzzetti A1 - Giorgio Mantica AB - 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 PB - 2007 Birkh¨auser Verlag Basel/Switzerland U1 - 6480 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Asymptotic variational wave equations JF - Arch. Ration. Mech. Anal. 183 (2007) 163-185 Y1 - 2007 A1 - Alberto Bressan A1 - Zhang Ping A1 - Zheng Yuxi AB - 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. UR - http://hdl.handle.net/1963/2182 U1 - 2062 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics Y1 - 2006 A1 - Claudio Altafini A1 - Francesco Ticozzi AB - 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. UR - http://hdl.handle.net/1963/1727 U1 - 2424 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An artificial viscosity approach to quasistatic crack growth Y1 - 2006 A1 - Rodica Toader A1 - Chiara Zanini AB - 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. UR - http://hdl.handle.net/1963/1850 U1 - 2367 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$ JF - Comm. Anal. Geom. 13 (2005) 187-252 Y1 - 2005 A1 - Sagun Chanillo A1 - Andrea Malchiodi AB - 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. PB - International Press UR - http://hdl.handle.net/1963/3533 U1 - 731 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the attainable set for Temple class systems with boundary controls JF - SIAM J. Control Optim. 43 (2005) 2166-2190 Y1 - 2005 A1 - Fabio Ancona A1 - Giuseppe Maria Coclite AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1581 U1 - 2537 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On almost duality for Frobenius manifolds JF - Amer. Math. Soc. Transl. 212 (2004)\\n75-132. Y1 - 2004 A1 - Boris Dubrovin AB - 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. UR - http://hdl.handle.net/1963/2543 U1 - 1576 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On analytic families of invariant tori for PDEs JF - Astérisque. Issue 297, 2004, Pages 35-65 Y1 - 2004 A1 - Boris Dubrovin AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6474 U1 - 6420 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains JF - Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. Y1 - 2004 A1 - Gianni Dal Maso A1 - Francois Murat AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1611 U1 - 2507 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations JF - Applied Math.Optim. 48 (2003), no.1, p.39-66 Y1 - 2003 A1 - Gianni Dal Maso A1 - Helene Frankowska PB - SISSA Library UR - http://hdl.handle.net/1963/1625 U1 - 2493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type JF - J. Differ. Equations, 2002, 180, 395 Y1 - 2002 A1 - Jean-Marc Mercier A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1491 U1 - 2672 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Arnold diffusion: a functional analysis approach JF - Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 43, Part 1, 2, Natsīonal. Akad. Nauk Ukraïni, Īnst. Mat., Kiev, 2002 Y1 - 2002 A1 - Massimiliano Berti AB - 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. PB - Natsīonal. Akad. Nauk Ukraïni U1 - 7269 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Adiabatic limits of closed orbits for some Newtonian systems in R-n JF - Asymptotic Anal., 2001, 25, 149-181 Y1 - 2001 A1 - Andrea Malchiodi AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1511 U1 - 2652 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Abnormal extremals for minimum time on the plane Y1 - 2000 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1508 U1 - 2655 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems Y1 - 2000 A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1554 U1 - 2564 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A(SLq(2)) at roots of unity is a free module over A(SL(2)) JF - Lett. Math. Phys., 2000, 52, 339 Y1 - 2000 A1 - Ludwik Dabrowski A1 - Cesare Reina A1 - Alessandro Zampa PB - SISSA Library UR - http://hdl.handle.net/1963/1500 U1 - 2663 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional JF - Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 Y1 - 1999 A1 - Matteo Negri AB - 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. PB - Taylor and Francis UR - http://hdl.handle.net/1963/1276 U1 - 3179 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Approximation, Stability and control for Conservation Laws Y1 - 1999 A1 - Andrea Marson PB - SISSA UR - http://hdl.handle.net/1963/5500 U1 - 5331 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains JF - Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 Y1 - 1999 A1 - Gianni Dal Maso A1 - Igor V. Skrypnik SN - 1618-1891 UR - http://hdl.handle.net/1963/6433 U1 - 6374 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - Algebraic Solutions to the Painlevé-VI Equation and Reflection Groups Y1 - 1998 A1 - Marta Mazzocco KW - Painlevé VI equation PB - SISSA UR - http://hdl.handle.net/1963/5574 U1 - 5402 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Asymptotic behavior of nonlinear Dirichlet problems in perforated domains JF - Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 Y1 - 1998 A1 - Gianni Dal Maso A1 - Igor V. Skrypnik PB - SISSA Library UR - http://hdl.handle.net/1963/1064 U1 - 2738 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Algebraic-geometrical Darboux coordinates in R-matrix formalism Y1 - 1994 A1 - P. Diener A1 - Boris Dubrovin PB - SISSA UR - http://hdl.handle.net/1963/3655 U1 - 650 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - Analysis of Singularity Structures for Quasi-Integrable Hamiltonian Systems Y1 - 1994 A1 - Simonetta Abenda KW - Hamiltonian systems PB - SISSA UR - http://hdl.handle.net/1963/5685 U1 - 5534 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - THES T1 - Asymptotic Behaviour of Dirichlet Problems in Perforated Domains Y1 - 1994 A1 - Adriana Garroni KW - Dirichlet problems PB - SISSA UR - http://hdl.handle.net/1963/5714 U1 - 5566 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Algebraic differential calculus for gauge theories JF - Nuclear Phys. B. Proc. Suppl. 18A (1990), 171 Y1 - 1990 A1 - Giovanni Landi A1 - Giuseppe Marmo PB - SISSA Library UR - http://hdl.handle.net/1963/891 U1 - 2900 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - An approach to the thin obstacle problem for variational functionals depending on vector JF - Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. Y1 - 1989 A1 - Gianni Dal Maso A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/802 U1 - 2989 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Algebraic reduction of the \\\'t Hooft-Polyakov monopole to the Dirac monopole. JF - Phys. Lett. B 201 (1988), no. 1, 101-104. Y1 - 1988 A1 - Giovanni Landi A1 - Giuseppe Marmo PB - SISSA Library UR - http://hdl.handle.net/1963/578 U1 - 3326 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - An Algebraic Setting for Gauge Theories Y1 - 1988 A1 - Giovanni Landi PB - SISSA UR - http://hdl.handle.net/1963/5828 U1 - 5677 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - On the asymptotic behaviour of solutions to Pazy\\\'s class of evolution equations Y1 - 1983 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/276 U1 - 3691 U2 - Mathematics U3 - Functional Analysis and Applications ER -