We study the degenerate linear Boltzmann equation inside a bounded domain with the Maxwell and the Cercignani-Lampis boundary conditions, two generalizations of the diffuse reflection, with variable temperature. We prove for the first time the existence of a steady state and a rate of convergence towards it without assumptions on the temperature variations.
Feb 1, 2025
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary condition. Our approach allows us to treat general domains with all types of boundary conditions (including the specular reflection boundary condition) in a unified framework.
Jul 13, 2022
This article was part of my PhD thesis, advised by Nicolas and Stéphane Mischler. You can find Nicolas’ webpage here.
Apr 1, 2022
This article is the starting point of my project focusing on the Cercignani-Lampis boundary condition in kinetic theory. You might also want to check the related preprint Asymptotic Behavior of Degenerate Linear Kinetic Equations with Non-Isothermal Boundary Conditions, where I consider collisional models with the same boundary conditions.
Mar 1, 2022
This article was part of my PhD thesis. One can find it as Chapter 5 of the volume LI of the “Séminaire de Probabilités”.
Jan 26, 2022
This article was part of my PhD thesis.
Nov 1, 2020