Convergence toward the steady state of a collisionless gas with Cercignani–Lampis boundary condition

We study the asymptotic behavior of kinetic free-transport equation enclosed in a regular domain, on which no symmetry assumption is made, with Cercignani–Lampis boundary condition. give first proof existence steady state case where temperature at wall varies, and derive optimal rate convergence toward it, L1 norm. The strategy an application deterministic version Harris’ subgeometric theorem, spirit recent results Cañizo-Mischler previous Bernou. also investigate rigorously velocity flow model mixing pure diffuse conditions variable temperature, for we explicit form state, providing new insights role condition this problem.