The Boltzmann equation with time-periodic boundary temperature
Abstract
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions with the same period for both hard and soft potentials, provided that the time-periodic boundary temperature is sufficiently close to a stationary one which has small variations around a positive constant. The dynamical stability of time-periodic profiles is also proved under small perturbations, and this in turn yields the non-negativity of the profile. For the proof, we develop new estimates in the time-periodic setting.
Cite
@article{arxiv.1807.07267,
title = {The Boltzmann equation with time-periodic boundary temperature},
author = {Renjun Duan and Yong Wang and Zhu Zhang},
journal= {arXiv preprint arXiv:1807.07267},
year = {2018}
}
Comments
36 pages. This paper is dedicated to Professor Philippe G. Ciarlet on the occasion of his 80th birthday