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, 2024
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