diamètre de classes d’espaces de Sobolev sur associés à des opérateurs de type «Schrödinger»
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
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.
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,...
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...
Klein Paradox and Superradiance for the charged Klein-Gordon Field
Klein-Gordon type decay rates for wave equations with time-dependent coefficients
This work is concerned with the proof of decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation . The coefficient consists of an increasing smooth function and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).
Koiter shell governed by strongly monotone constitutive equations
In this paper we use the theory of monotone operators to generalize the linear shell model presented in (Blouza and Le Dret, 1999) to a class of physically nonlinear models. We present a family of nonlinear constitutive equations, for which we prove the existence and uniqueness of the solution of the presented nonlinear model, as well as the convergence of the Galerkin method. We also present the physical discussion of the model.
KP trigonometric solitons and an adelic flag manifold.
Krylov subspace acceleration for nonlinear multigrid schemes.
Kuramoto-Sivashinsky equation in domains with moving boundaries.