Convergence Towards the Steady State of a Collisionless Gas With CercignaniLampis Boundary Condition
Abstract
We study the asymptotic behavior of the kinetic freetransport equation enclosed in a regular domain, on which no symmetry assumption is made, with CercignaniLampis boundary condition. We give the first proof of existence of a steady state in the case where the temperature at the wall varies, and derive the optimal rate of convergence towards it, in the L1 norm. The strategy is an application of a deterministic version of Harris subgeometric theorem, in the spirit of CañizoMischler (2021) and Bernou (2020). We also investigate rigorously the velocity flow of a model mixing pure diffuse and CercignaniLampis boundary conditions with variable temperature, for which we derive an explicit form for the steady state, providing new insights on the role of the CercignaniLampis boundary condition in this problem.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.06284
 arXiv:
 arXiv:2106.06284
 Bibcode:
 2021arXiv210606284B
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 35B40;
 82C40 (Primary) 35C05;
 35F16;
 35Q49 (Secondary)
 EPrint:
 40 pages, 1 figure