In this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N\<\infty$, the entropic cost (i.e. the minimal value of the Schr{\"o}dinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou{\textendash}Brenier formula for the Wasserstein distance; A Hamilton{\textendash}Jacobi{\textendash}Bellman dual representation, in line with Bobkov{\textendash}Gentil{\textendash}Ledoux and Otto{\textendash}Villani results on the duality between Hamilton{\textendash}Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf{\textendash}Lax semigroup is replaced by a suitable {\textquoteleft}entropic{\textquoteright} counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schr{\"o}dinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.

}, issn = {1432-2064}, doi = {10.1007/s00440-019-00909-1}, url = {https://doi.org/10.1007/s00440-019-00909-1}, author = {Nicola Gigli and Luca Tamanini} } @article {GIULIANI2019324, title = {BlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D}, journal = {Computer Physics Communications}, volume = {235}, year = {2019}, pages = {324 - 335}, abstract = {Many applications benefit from an efficient Discrete Fourier Transform (DFT) between arbitrarily spaced points. The Non Uniform Fast Fourier Transform reduces the computational cost of such operation from O(N2) to O(NlogN) exploiting gridding algorithms and a standard Fast Fourier Transform on an equi-spaced grid. The parallelization of the NUFFT of type 3 (between arbitrary points in space and frequency) still poses some challenges: we present a novel and flexible hybrid parallelization in a MPI-multithreaded environment exploiting existing HPC libraries on modern architectures. To ensure the reliability of the developed library, we exploit continuous integration strategies using Travis CI. We present performance analyses to prove the effectiveness of our implementation, possible extensions to the existing library, and an application of NUFFT type 3 to MRI image processing. Program summary Program Title: BlackNUFFT Program Files doi: http://dx.doi.org/10.17632/vxfj6x2p8x.1 Licensing provisions: LGPL Programming language: C++ External routines/libraries: deal.II , FFTW, PFFT Nature of problem: Provide a modular and extensible implementation of a parallel Non Uniform Fast Fourier Transform of type 3. Solution method: Use of hybrid shared distributed memory paradigm to achieve high level of efficiency. We exploit existing HPC library following best practices in scientific computing (as continuous integration via TravisCI) to reach higher complexities and guarantee the accuracy of the solution proposed.

}, keywords = {C++, Extensibility, FFT, Modularity, MPI, MRI image processing, NUFFT type 3, TBB}, issn = {0010-4655}, doi = {https://doi.org/10.1016/j.cpc.2018.10.005}, url = {http://www.sciencedirect.com/science/article/pii/S0010465518303539}, author = {Nicola Giuliani} } @article {2018arXiv180705892A, title = {The Baum{\textendash}Connes conjecture localised at the unit element of a discrete group}, journal = {ArXiv e-prints}, year = {2018}, keywords = {19K35, 46L80, 46L85, 58J22, Mathematics - K-Theory and Homology, Mathematics - Operator Algebras}, author = {Paolo Antonini and Azzali, S. and Skandalis, G.} } @article {1607.05188, title = {Behaviour of the reference measure on RCD spaces under charts}, year = {2016}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {2015, title = {Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems}, journal = {Computers and Mathematics with Applications 69 (2015) 1167{\textendash}1188}, number = {;69}, year = {2015}, abstract = {We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks.}, doi = {10.1016/j.camwa.2015.03.012}, author = {Roy Saswati and Luca Heltai and Francesco Costanzo} } @article {2015, title = {A bridging mechanism in the homogenisation of brittle composites with soft inclusions}, number = {SISSA;02/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.}, url = {http://urania.sissa.it/xmlui/handle/1963/7492}, author = {Marco Barchiesi and Giuliano Lazzaroni and Caterina Ida Zeppieri} } @article {2014, title = {Buckling dynamics of a solvent-stimulated stretched elastomeric sheet}, number = {Soft Matter;volume 10; issue 16; pages 2800-2804;}, year = {2014}, publisher = {Royal Society of Chemistry}, abstract = {When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet.}, doi = {10.1039/c3sm52941j}, url = {http://urania.sissa.it/xmlui/handle/1963/34967}, author = {Alessandro Lucantonio and Matthieu Roch{\'e} and Paola Nardinocchi and Howard A. Stone} } @mastersthesis {2013, title = {Biregular and Birational Geometry of Algebraic Varieties}, year = {2013}, school = {SISSA}, abstract = {Every area of mathematics is characterized by a guiding problem. In algebraic geometry such problem is the classification of algebraic varieties. In its strongest form it means to classify varieties up to biregular morphisms. However, birationally equivalent varieties share many interesting properties. Therefore for any birational equivalence class it is natural to work out a variety, which is the simplest in a suitable sense, and then study these varieties. This is the aim of birational geometry. In the first part of this thesis we deal with the biregular geometry of moduli spaces of curves, and in particular with their biregular automorphisms. However, in doing this we will consider some aspects of their birational geometry. The second part is devoted to the birational geometry of varieties of sums of powers and to some related problems which will lead us to computational geometry and geometric complexity theory.}, keywords = {Moduli spaces of curves, automorphisms, Hassett{\textquoteright}s moduli spaces, varieties of sums of powers}, author = {Alex Massarenti} } @article {2012, title = {On the behaviour of flexible retaining walls under seismic actions}, journal = {Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094}, year = {2012}, publisher = {ICE Publishing}, abstract = {This paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value.}, keywords = {Centrifuge modelling}, doi = {10.1680/geot.11.P.029}, url = {http://hdl.handle.net/1963/6933}, author = {Riccardo Conti and G.S.P. Madabhushi and Giulia M.B. Viggiani} } @article {2012, title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty}, journal = {Mathematical Modelling and Numerical Analysis, in press, 2012-13}, number = {SISSA;42/2012/M}, year = {2012}, publisher = {Cambridge University Press}, abstract = {We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.}, keywords = {shape optimization}, url = {http://hdl.handle.net/1963/6337}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2011, title = {Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry}, year = {2011}, note = {25 pages}, publisher = {SISSA}, abstract = {We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.}, url = {http://hdl.handle.net/1963/6508}, author = {Andrei A. Agrachev and Paul Lee} } @article {Bertola:Boutroux, title = {Boutroux curves with external field: equilibrium measures without a variational problem}, journal = {Anal. Math. Phys.}, volume = {1}, number = {2-3}, year = {2011}, pages = {167{\textendash}211}, issn = {1664-2368}, doi = {10.1007/s13324-011-0012-3}, url = {http://dx.doi.org/10.1007/s13324-011-0012-3}, author = {Marco Bertola} } @article {Berti2011741, title = {Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs}, journal = {Communications in Mathematical Physics}, volume = {305}, number = {3}, year = {2011}, note = {cited By (since 1996)8}, pages = {741-796}, abstract = {We consider infinite dimensional Hamiltonian systems. We prove the existence of "Cantor manifolds" of elliptic tori-of any finite higher dimension-accumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence of Cantor manifolds of elliptic tori which are "branching" points of other Cantor manifolds of higher dimensional tori. We also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear wave equation. {\textcopyright} 2011 Springer-Verlag.}, issn = {00103616}, doi = {10.1007/s00220-011-1264-3}, author = {Massimiliano Berti and Luca Biasco} } @inbook {2009, title = {Biological Fluid Dynamics, Non-linear Partial Differential Equations}, booktitle = {Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554}, number = {SISSA;21/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2630}, author = {Antonio DeSimone and Fran{\c c}ois Alouges and Aline Lefebvre} } @article {2009, title = {The boundary Riemann solver coming from the real vanishing viscosity approximation}, journal = {Arch. Ration. Mech. Anal. 191 (2009) 1-96}, number = {SISSA;24/2006/M}, year = {2009}, abstract = {We study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.}, doi = {10.1007/s00205-008-0177-6}, url = {http://hdl.handle.net/1963/1831}, author = {Stefano Bianchini and Laura Spinolo} } @article {2009, title = {Bubbles with prescribed mean curvature: the variational approach}, number = {SISSA;35/2009/M}, year = {2009}, note = {H-systems, prescribed mean curvature equation, blowup}, url = {http://hdl.handle.net/1963/3659}, author = {Paolo Caldiroli and Roberta Musina} } @article {Bertola:LOPs, title = {Biorthogonal Laurent polynomials, T{\"o}plitz determinants, minimal Toda orbits and isomonodromic tau functions}, journal = {Constr. Approx.}, volume = {26}, number = {3}, year = {2007}, pages = {383{\textendash}430}, issn = {0176-4276}, author = {Marco Bertola and Gekhtman, M.} } @article {Bertola:semiclassBOPsJAT, title = {Biorthogonal polynomials for two-matrix models with semiclassical potentials}, journal = {J. Approx. Theory}, volume = {144}, number = {2}, year = {2007}, pages = {162{\textendash}212}, issn = {0021-9045}, author = {Marco Bertola} } @article {2007, title = {Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory}, number = {SISSA;61/2006/FM}, year = {2007}, abstract = {We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.}, doi = {10.1016/j.nuclphysb.2007.02.030}, url = {http://hdl.handle.net/1963/1888}, author = {Luca Griguolo and Domenico Seminara and Richard J. Szabo and Alessandro Tanzini} } @article {2007, title = {Bose-Einstein condensation: analysis of problems and rigorous results}, number = {SISSA;70/2007/MP}, year = {2007}, url = {http://hdl.handle.net/1963/2189}, author = {Alessandro Michelangeli} } @article {2007, title = {Boundary interface for the Allen-Cahn equation}, journal = {J. Fixed Point Theory Appl. 1 (2007) 305-336}, year = {2007}, doi = {10.1007/s11784-007-0016-7}, url = {http://hdl.handle.net/1963/2027}, author = {Andrea Malchiodi and Juncheng Wei} } @article {2007, title = {Boundary-clustered interfaces for the Allen{\textendash}Cahn equation}, journal = {Pacific Journal of Mathematics 229 (2007), No. 2, 447{\textendash}468}, year = {2007}, publisher = {Mathematical Sciences Publishers}, url = {http://hdl.handle.net/1963/5089}, author = {Andrea Malchiodi and Wei-Ming Ni and Juncheng Wei} } @article {2007, title = {BV instability for the Lax-Friedrichs scheme}, number = {SISSA;100/2004/M}, year = {2007}, abstract = {It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.}, url = {http://hdl.handle.net/1963/2335}, author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen} } @article {2006, title = {A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs}, journal = {SIAM J. Math. Anal. 37 (2006) 83-102}, number = {arXiv.org;math/0310182v1}, year = {2006}, abstract = {In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.}, doi = {10.1137/S0036141003436107}, url = {http://hdl.handle.net/1963/2159}, author = {Dario Bambusi and Massimiliano Berti} } @article {2006, title = {Born approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation}, number = {SISSA;13/2006/FM}, year = {2006}, abstract = {\\\"It has a flavour of Mathematical Physics...\\\"With these words, just few years ago, prof. Di Giacomo\\nused to introduce the topic of the Born approximation within a nonrelativistic potential theory, in his {\textquoteleft}oversize\\\' course of Theoretical Physics in Pisa. Something maybe too fictitious inside the formal theory of the scattering he was teaching us at that point of the course. Now that I\\\'m (studying to become) a Mathematical Physicist indeed, dealing with such an {\textquoteleft}exotic tasting\\\' topic, those words come back to the mind, into a new perspective. Here the very recent problem of the rigorous derivation of\\nthe cubic nonlinear Schr{\"o}dinger equation (the Gross-Pitaevski{\^\i} equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit}, url = {http://hdl.handle.net/1963/1819}, author = {Alessandro Michelangeli} } @article {2006, title = {Bound and ground states of coupled nonlinear Schr{\"o}dinger equations}, journal = {C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458}, year = {2006}, abstract = {We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations.}, doi = {10.1016/j.crma.2006.01.024}, url = {http://hdl.handle.net/1963/2149}, author = {Antonio Ambrosetti and Eduardo Colorado} } @article {2006, title = {Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity}, journal = {J. Anal. Math. 98 (2006) 317-348}, number = {SISSA;18/2005/M}, year = {2006}, doi = {10.1007/BF02790279}, url = {http://hdl.handle.net/1963/1756}, author = {Antonio Ambrosetti and Andrea Malchiodi and David Ruiz} } @article {2006, title = {On Bressan\\\'s conjecture on mixing properties of vector fields}, journal = {Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31}, number = {SISSA;70/2005/M}, year = {2006}, url = {http://hdl.handle.net/1963/1806}, author = {Stefano Bianchini} } @article {2005, title = {On the Blow-up for a Discrete Boltzmann Equation in the Plane}, journal = {Discrete Contin. Dyn. Syst. 13 (2005) 1-12}, number = {arXiv.org;math/0403047v2}, year = {2005}, abstract = {We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.}, url = {http://hdl.handle.net/1963/2244}, author = {Alberto Bressan and Massimo Fonte} } @article {2004, title = {Bifurcation of free vibrations for completely resonant wave equations}, journal = {Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528}, number = {SISSA;27/2004/M}, year = {2004}, abstract = {We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.}, url = {http://hdl.handle.net/1963/2245}, author = {Massimiliano Berti and Philippe Bolle} } @article {2004, title = {Blow-up solutions for the Schr{\"o}dinger equation in dimension three with a concentrated nonlinearity}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137}, year = {2004}, publisher = {Elsevier}, abstract = {We present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions.}, doi = {10.1016/j.anihpc.2003.01.002}, url = {http://hdl.handle.net/1963/2998}, author = {Riccardo Adami and Gianfausto Dell{\textquoteright}Antonio and Rodolfo Figari and Alessandro Teta} } @article {Bertola:BilinearJAT, title = {Bilinear semiclassical moment functionals and their integral representation}, journal = {J. Approx. Theory}, volume = {121}, number = {1}, year = {2003}, pages = {71{\textendash}99}, issn = {0021-9045}, author = {Marco Bertola} } @article {2002, title = {On the Boundary Control of Systems of Conservation Laws}, journal = {SIAM J. Control Optim. 41 (2002) 607-622}, number = {SISSA;50/2001/M}, year = {2002}, publisher = {SIAM}, abstract = {The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.}, doi = {10.1137/S0363012901392529}, url = {http://hdl.handle.net/1963/3070}, author = {Alberto Bressan and Giuseppe Maria Coclite} } @article {2001, title = {Bihamiltonian geometry and separation of variables for Toda lattices}, journal = {J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127}, number = {SISSA;139/99/FM}, year = {2001}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1354}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni} } @article {2000, title = {A bi-Hamiltonian theory for stationary KDV flows and their separability}, journal = {Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52}, number = {SISSA;137/99/FM}, year = {2000}, publisher = {SISSA Library}, doi = {10.1070/rd2000v005n01ABEH000122}, url = {http://hdl.handle.net/1963/1352}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni and Jorge P. Zubelli} } @article {2000, title = {BV estimates for multicomponent chromatography with relaxation}, journal = {Discrete Contin. Dynam. Systems 6 (2000) 21-38}, number = {SISSA;122/99/M}, year = {2000}, publisher = {SISSA Library}, abstract = {We consider the Cauchy problem for a system of $2n$ balance laws which arises from the modelling of multi-component chromatography: $$\\\\left\\\\{ \\\\eqalign{u_t+u_x\&=-{1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr v_t\&={1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr}\\\\right. \\\\eqno(1)$$ This model describes a liquid flowing with unit speed over a solid bed. Several chemical substances are partly dissolved in the liquid, partly deposited on the solid bed. Their concentrations are represented respectively by the vectors $u=(u_1,\\\\ldots,u_n)$ and $v=(v_1,\\\\ldots,v_n)$. We show that, if the initial data have small total variation, then the solution of (1) remains with small variation for all times $t\\\\geq 0$. Moreover, using the $\\\\L^1$ distance, this solution depends Lipschitz continuously on the initial data, with a Lipschitz constant uniform w.r.t.~$\\\\ve$. Finally we prove that as $\\\\ve\\\\to 0$, the solutions of (1) converge to a limit described by the system $$\\\\big(u+F(u)\\\\big)_t+u_x=0,\\\\qquad\\\\qquad v=F(u).\\\\eqno(2)$$ The proof of the uniform BV estimates relies on the application of probabilistic techniques. It is shown that the components of the gradients $v_x,u_x$ can be interpreted as densities of random particles travelling with speed 0 or 1. The amount of coupling between different components is estimated in terms of the expected number of crossing of these random particles. This provides a first example where BV estimates are proved for general solutions to a class of $2n\\\\times 2n$ systems with relaxation.}, url = {http://hdl.handle.net/1963/1336}, author = {Alberto Bressan and Wen Shen} } @article {2000, title = {BV solutions for a class of viscous hyperbolic systems}, journal = {Indiana Univ. Math. J. 49 (2000) 1673-1714}, year = {2000}, publisher = {Indiana University Mathematics Journal}, doi = {10.1512/iumj.2000.49.1776}, url = {http://hdl.handle.net/1963/3194}, author = {Stefano Bianchini and Alberto Bressan} } @inbook {1999, title = {A bihamiltonian approach to separation of variables in mechanics}, booktitle = {Proceedings of the workshop on nonlinearity, integrability and all that : twenty years after NEEDS \\\'79, Lecce, Italy, July 1 - 10, 1999 / ed. by M. Boiti. - Singapore : World Scientific, 2000. - p. 258-266}, year = {1999}, publisher = {World Scientific}, organization = {World Scientific}, abstract = {This paper is a report on a recent approach to the theory of separability of the Hamilton-Jacobi equations from the viewpoint of bihamiltonian geometry.}, url = {http://hdl.handle.net/1963/3222}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni} } @article {1999, title = {Blowup asymptotics for scalar conservation laws with a source}, journal = {Comm. in Partial Differential Equations 24 (1999) 2237-2261}, number = {SISSA;91/97/M}, year = {1999}, publisher = {Taylor and Francis}, doi = {10.1080/03605309908821500}, url = {http://hdl.handle.net/1963/3482}, author = {Helge Kristian Jenssen and Carlo Sinestrari} } @article {1998, title = {Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation}, journal = {Comm. Math. Phys. 198 (1998) 311-361}, number = {SISSA;152/97/FM}, year = {1998}, publisher = {Springer}, abstract = {We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov - Witten invariants via tau-function of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity.}, doi = {10.1007/s002200050480}, url = {http://hdl.handle.net/1963/3696}, author = {Boris Dubrovin and Zhang Youjin} } @article {1998, title = {Branching points for a class of variational operators}, journal = {J. Anal. Math. 76 (1998) 321-335}, year = {1998}, publisher = {Springer}, doi = {10.1007/BF02786940}, url = {http://hdl.handle.net/1963/3314}, author = {Antonio Ambrosetti} } @article {1993, title = {A Borel-Weil-Bott approach to representations of {\rm sl}\sb q(2,C)}, journal = {Lett. Math. Phys. 29 (1993) 215-217}, number = {SISSA;58/93/FM}, year = {1993}, publisher = {Springer}, abstract = {We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.

}, doi = {10.1007/BF00761109}, url = {http://hdl.handle.net/1963/3538}, author = {Davide Franco and Cesare Reina} }