diamètre de classes d’espaces de Sobolev sur associés à des opérateurs de type «Schrödinger»
Kac functional and Schrödinger equation
Kac-Moody groups and integrability of soliton equations.
Kac’s chaos and Kac’s program
In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.
KAM techniques in PDE
KAM theory for the hamiltonian derivative wave equation
We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.
KAM theory in momentum space and quasiperiodic Schrödinger operators
Kazhdan-Lusztig Conjecture and Holonomic Systems.
KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions
The matrix KdV equation with a negative dispersion term is considered in the right upper quarter–plane. The evolution law is derived for the Weyl function of a corresponding auxiliary linear system. Using the low energy asymptotics of the Weyl functions, the unboundedness of solutions is obtained for some classes of the initial–boundary conditions.
Kelvin principle for a class of singular equations.
Killing spinor-valued forms and the cone construction
On a pseudo-Riemannian manifold we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on and parallel fields on the metric cone over for spinor-valued forms.
Kinetic approach to systems of conservation laws
Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium
This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness of the discrete velocity model is demonstrated. Thus, the convergence of the solution to that...
Kinetic equations with Maxwell boundary conditions
We prove global stability results of DiPerna-Lionsrenormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which includes the so-called Maxwell boundary conditions, and we prove that it is realized (it is not only a boundary inequality condition as it has been established in previous works). We are able to deal with Boltzmann,...
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.
The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogencous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities,...
Kinetic formulation for heterogeneous scalar conservation laws
Kink solutions of the binormal flow
I shall present some recent work in collaboration with S. Gutierrez on the characterization of all selfsimilar solutions of the binormal flow : which preserve the length parametrization. Above is a curve in , the arclength parameter, and denote the temporal variable. This flow appeared for the first time in the work of Da Rios (1906) as a crude approximation to the evolution of a vortex filament under Euler equation, and it is intimately related to the focusing cubic nonlinear Schrödinger...
Kink-antikink interaction for semilinear wave equations with a small parameter.
Kirchhoff-Carrier elastic strings in noncylindrical domains.
Klassische Lösungen im Großen semilinearen parabolischer Differentialgleichungen.