Related papers: Hypocoercivity for kinetic equations with linear r…
We propose a BGK-type kinetic model for a binary gas mixture, designed to serve as a kinetic formulation of compressible two-phase fluid dynamics. The model features species-dependent adiabatic exponents, and the relaxation operator is…
In this article, we propose a finite volume discretization of a one dimensional nonlinear reaction kinetic model proposed in [Neumann, Schmeiser, Kint. Rel. Mod. 2016], which describes a 2-species recombination-generation process.…
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes…
We prove the consistency of Galerkin methods to solve Poisson equations where the differential operator under consideration is the generator of the Langevin dynamics. We show in particular how the hypocoercive nature of this operator can be…
In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using…
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of inhomogeneous…
We establish global hypoelliptic estimates for linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau…
By further developing the generalized $\Gamma$-calculus for hypoelliptic operators, we prove hypocoercive estimates for a large class of Kolmogorov type operators which are defined on non necessarily totally geodesic Riemannian foliations.…
The aim of this article is to construct solutions to second order in time stochastic partial differential equations and to show hypocoercivity of the corresponding transition semigroups. More generally, we analyze non-linear…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…
We study the linearized kinetic equation of relaxation model which was proposed by Bhatnagar, Gross and Krook (also called BGK model) and solve the dispersion relation. Using the solution of the dispersion relation, we analyze the…
We present the quantitative method of the recent work arXiv:2209.09340 in a simple setting, together with a compactness argument that was not included in arXiv:2209.09340 and has interest per se. We are concerned with the exponential…
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
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 boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…
This note provides a simple derivation of the overdamped approximation for kinetic (or underdamped) equilibrium Langevin dynamics, in cases where certain coefficients depend on the position variable. The equivalent small-mass limit of these…
We present a high order scheme for approximating kinetic equations with stiff relaxation. The objective is to provide efficient methods for solving the underlying system of conservation laws. The construction is based on several…