相关论文: Exponential convergence to equilibrium for kinetic…
In this note, we consider a kinetic Fokker-Planck-Alignment equation with Rayleigh-type friction and self-propulsion force which is derived from general environmental averaging models. We show the exponential relaxation in time toward…
This paper is concerned with a modified entropy method to establish the large-time convergence towards the (unique) steady state, for kinetic Fokker-Planck equations with non-quadratic confinement potentials in whole space. We extend…
We consider the relativistic, spatially inhomogeneous Fokker-Planck equation with an external confining potential. We prove the exponential time decay of solutions towards the global equilibrium in weighted $L^2$ and Sobolov spaces. Our…
The relativistic Fokker-Planck equation, in which the speed of light $c$ appears as a parameter, is considered. It is shown that in the limit $c\to\infty$ its solutions converge in $L^1$ to solutions of the non-relativistic Fokker-Planck…
We prove the exponential convergence to the equilibrium, quantified by R\'enyi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictly convex potential. This extends the classical exponential…
In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $N\ge 2$ is the number of vertices of the graph, they show that the corresponding…
We consider the Fokker-Planck equation with a strong external magnetic field. Global-in-time solutions are built near the Maxwellian, the global equilibrium state for the system. Moreover, we prove the convergence to equilibrium at…
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…
This paper is concerned with finding Fokker-Planck equations in $\mathbb{R}^d$ with the fastest exponential decay towards a given equilibrium. For a prescribed, anisotropic Gaussian we determine a non-symmetric Fokker-Planck equation with…
We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation. We prove a uniform (in the number of particles) exponential convergence to…
We study a nonlocal approximation of the Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium in a way which does not degenerate as we approach the local limit of the equation. This uniform estimate cannot…
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence…
We consider the kinetic Fokker-Planck equation with a class of general force. We prove the existence and uniqueness of a positive normalized equilibrium (in the case of a general force) and establish some exponential rate of convergence to…
We study the relaxation to equilibrium for a class linear one-dimensional Fokker-Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker-Planck equations is that, for…
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global well-posedness result with instantaneous smoothness effect,…
This paper concerns the proof of the exponential rate of convergence of the solution of a Fokker-Planck equation, with a drift term not being the gradient of a potential function and endowed by Robin type boundary conditions. This kind of…
The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a…
We prove long-time contractivity estimates and exponential rates of convergence to equilibrium for solutions of hypoelliptic diffusion equations, which include the well-known Kolmogorov equation and similar kinetic Fokker-Planck equations…
We first prove a homogenization result for the fundamental solution of the linear kinetic Fokker Planck equation. We show that this solution converges, in an averaged $L^2$ sense, to the fundamental solution of an effective heat equation…
We study the solution of the two-temperatures Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of…