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 Schrödinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou–Brenier formula for the Wasserstein distance; A Hamilton–Jacobi–Bellman dual representation, in line with Bobkov–Gentil–Ledoux and Otto–Villani results on the duality between Hamilton–Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf–Lax semigroup is replaced by a suitable `entropic' counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schrödinger 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.

UR - https://doi.org/10.1007/s00440-019-00909-1 ER - TY - JOUR T1 - BlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D JF - Computer Physics Communications Y1 - 2019 A1 - Nicola Giuliani KW - C++ KW - Extensibility KW - FFT KW - Modularity KW - MPI KW - MRI image processing KW - NUFFT type 3 KW - TBB AB -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.

VL - 235 UR - http://www.sciencedirect.com/science/article/pii/S0010465518303539 ER - TY - JOUR T1 - The Baum–Connes conjecture localised at the unit element of a discrete group JF - ArXiv e-prints Y1 - 2018 A1 - Paolo Antonini A1 - Azzali, S. A1 - Skandalis, G. KW - 19K35 KW - 46L80 KW - 46L85 KW - 58J22 KW - Mathematics - K-Theory and Homology KW - Mathematics - Operator Algebras ER - TY - RPRT T1 - Behaviour of the reference measure on RCD spaces under charts Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems JF - Computers and Mathematics with Applications 69 (2015) 1167–1188 Y1 - 2015 A1 - Roy Saswati A1 - Luca Heltai A1 - Francesco Costanzo AB - 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. U1 - 34633 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - A bridging mechanism in the homogenisation of brittle composites with soft inclusions Y1 - 2015 A1 - Marco Barchiesi A1 - Giuliano Lazzaroni A1 - Caterina Ida Zeppieri AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7492 U1 - 7621 ER - TY - JOUR T1 - Buckling dynamics of a solvent-stimulated stretched elastomeric sheet Y1 - 2014 A1 - Alessandro Lucantonio A1 - Matthieu Roché A1 - Paola Nardinocchi A1 - Howard A. Stone AB - 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. PB - Royal Society of Chemistry UR - http://urania.sissa.it/xmlui/handle/1963/34967 U1 - 35197 U2 - Physics U4 - 1 ER - TY - THES T1 - Biregular and Birational Geometry of Algebraic Varieties Y1 - 2013 A1 - Alex Massarenti KW - Moduli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers AB - 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. PB - SISSA U1 - 6962 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - On the behaviour of flexible retaining walls under seismic actions JF - Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 Y1 - 2012 A1 - Riccardo Conti A1 - G.S.P. Madabhushi A1 - Giulia M.B. Viggiani KW - Centrifuge modelling AB - 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. PB - ICE Publishing UR - http://hdl.handle.net/1963/6933 U1 - 6912 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty JF - Mathematical Modelling and Numerical Analysis, in press, 2012-13 Y1 - 2012 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - shape optimization AB - 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. PB - Cambridge University Press UR - http://hdl.handle.net/1963/6337 U1 - 6267 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry Y1 - 2011 A1 - Andrei A. Agrachev A1 - Paul Lee AB - We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry. PB - SISSA UR - http://hdl.handle.net/1963/6508 N1 - 25 pages U1 - 6455 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Boutroux curves with external field: equilibrium measures without a variational problem JF - Anal. Math. Phys. Y1 - 2011 A1 - Marco Bertola VL - 1 UR - http://dx.doi.org/10.1007/s13324-011-0012-3 ER - TY - JOUR T1 - Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs JF - Communications in Mathematical Physics Y1 - 2011 A1 - Massimiliano Berti A1 - Luca Biasco AB - 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. © 2011 Springer-Verlag. VL - 305 N1 - cited By (since 1996)8 ER - TY - CHAP T1 - Biological Fluid Dynamics, Non-linear Partial Differential Equations T2 - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 Y1 - 2009 A1 - Antonio DeSimone A1 - François Alouges A1 - Aline Lefebvre JF - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 UR - http://hdl.handle.net/1963/2630 U1 - 1493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The boundary Riemann solver coming from the real vanishing viscosity approximation JF - Arch. Ration. Mech. Anal. 191 (2009) 1-96 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Spinolo AB - 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. UR - http://hdl.handle.net/1963/1831 U1 - 2385 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Bubbles with prescribed mean curvature: the variational approach Y1 - 2009 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/3659 N1 - H-systems, prescribed mean curvature equation, blowup U1 - 646 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Biorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions JF - Constr. Approx. Y1 - 2007 A1 - Marco Bertola A1 - Gekhtman, M. VL - 26 ER - TY - JOUR T1 - Biorthogonal polynomials for two-matrix models with semiclassical potentials JF - J. Approx. Theory Y1 - 2007 A1 - Marco Bertola VL - 144 ER - TY - RPRT T1 - Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory Y1 - 2007 A1 - Luca Griguolo A1 - Domenico Seminara A1 - Richard J. Szabo A1 - Alessandro Tanzini AB - 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. JF - Nucl. Phys. B 772 (2007) 1-24 UR - http://hdl.handle.net/1963/1888 U1 - 2347 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Bose-Einstein condensation: analysis of problems and rigorous results Y1 - 2007 A1 - Alessandro Michelangeli UR - http://hdl.handle.net/1963/2189 U1 - 2055 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Boundary interface for the Allen-Cahn equation JF - J. Fixed Point Theory Appl. 1 (2007) 305-336 Y1 - 2007 A1 - Andrea Malchiodi A1 - Juncheng Wei UR - http://hdl.handle.net/1963/2027 U1 - 2169 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Boundary-clustered interfaces for the Allen–Cahn equation JF - Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 Y1 - 2007 A1 - Andrea Malchiodi A1 - Wei-Ming Ni A1 - Juncheng Wei PB - Mathematical Sciences Publishers UR - http://hdl.handle.net/1963/5089 U1 - 4905 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - BV instability for the Lax-Friedrichs scheme Y1 - 2007 A1 - Paolo Baiti A1 - Alberto Bressan A1 - Helge Kristian Jenssen AB - 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. UR - http://hdl.handle.net/1963/2335 U1 - 1681 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs JF - SIAM J. Math. Anal. 37 (2006) 83-102 Y1 - 2006 A1 - Dario Bambusi A1 - Massimiliano Berti AB - 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. UR - http://hdl.handle.net/1963/2159 U1 - 2085 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Born approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation Y1 - 2006 A1 - Alessandro Michelangeli AB - \\\"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 `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 `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 Schrödinger equation (the Gross-Pitaevskiî equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit UR - http://hdl.handle.net/1963/1819 U1 - 2395 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Bound and ground states of coupled nonlinear Schrödinger equations JF - C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 Y1 - 2006 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations. UR - http://hdl.handle.net/1963/2149 U1 - 2094 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity JF - J. Anal. Math. 98 (2006) 317-348 Y1 - 2006 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - David Ruiz UR - http://hdl.handle.net/1963/1756 U1 - 2788 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On Bressan\\\'s conjecture on mixing properties of vector fields JF - Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31 Y1 - 2006 A1 - Stefano Bianchini UR - http://hdl.handle.net/1963/1806 U1 - 2408 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Blow-up for a Discrete Boltzmann Equation in the Plane JF - Discrete Contin. Dyn. Syst. 13 (2005) 1-12 Y1 - 2005 A1 - Alberto Bressan A1 - Massimo Fonte AB - 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. UR - http://hdl.handle.net/1963/2244 U1 - 2000 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bifurcation of free vibrations for completely resonant wave equations JF - Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528 Y1 - 2004 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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. UR - http://hdl.handle.net/1963/2245 U1 - 1999 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity JF - Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137 Y1 - 2004 A1 - Riccardo Adami A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/2998 U1 - 1335 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Bilinear semiclassical moment functionals and their integral representation JF - J. Approx. Theory Y1 - 2003 A1 - Marco Bertola VL - 121 ER - TY - JOUR T1 - On the Boundary Control of Systems of Conservation Laws JF - SIAM J. Control Optim. 41 (2002) 607-622 Y1 - 2002 A1 - Alberto Bressan A1 - Giuseppe Maria Coclite AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/3070 U1 - 1263 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bihamiltonian geometry and separation of variables for Toda lattices JF - J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127 Y1 - 2001 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni PB - SISSA Library UR - http://hdl.handle.net/1963/1354 U1 - 3101 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A bi-Hamiltonian theory for stationary KDV flows and their separability JF - Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52 Y1 - 2000 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni A1 - Jorge P. Zubelli PB - SISSA Library UR - http://hdl.handle.net/1963/1352 U1 - 3103 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - BV estimates for multicomponent chromatography with relaxation JF - Discrete Contin. Dynam. Systems 6 (2000) 21-38 Y1 - 2000 A1 - Alberto Bressan A1 - Wen Shen AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1336 U1 - 3119 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - BV solutions for a class of viscous hyperbolic systems JF - Indiana Univ. Math. J. 49 (2000) 1673-1714 Y1 - 2000 A1 - Stefano Bianchini A1 - Alberto Bressan PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/3194 U1 - 1107 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - A bihamiltonian approach to separation of variables in mechanics T2 - 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 Y1 - 1999 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni AB - 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. JF - 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 PB - World Scientific UR - http://hdl.handle.net/1963/3222 U1 - 1079 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Blowup asymptotics for scalar conservation laws with a source JF - Comm. in Partial Differential Equations 24 (1999) 2237-2261 Y1 - 1999 A1 - Helge Kristian Jenssen A1 - Carlo Sinestrari PB - Taylor and Francis UR - http://hdl.handle.net/1963/3482 U1 - 782 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation JF - Comm. Math. Phys. 198 (1998) 311-361 Y1 - 1998 A1 - Boris Dubrovin A1 - Zhang Youjin AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3696 U1 - 609 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Branching points for a class of variational operators JF - J. Anal. Math. 76 (1998) 321-335 Y1 - 1998 A1 - Antonio Ambrosetti PB - Springer UR - http://hdl.handle.net/1963/3314 U1 - 1016 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Borel-Weil-Bott approach to representations of \rm sl\sb q(2,C) JF - Lett. Math. Phys. 29 (1993) 215-217 Y1 - 1993 A1 - Davide Franco A1 - Cesare Reina AB -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.

PB - Springer UR - http://hdl.handle.net/1963/3538 U1 - 1163 U2 - Mathematics U3 - Mathematical Physics ER -