Hypocoercivity of the linearized BGK-equation with stochastic coefficients
Analysis of PDEs
2023-10-09 v3
Abstract
In this paper we study the effect of randomness on a linearized BGK-model in one dimension. We prove exponential decay rate to a global equilibrium. This decay rate can be proven to be independent of the stochastic influence in a physical reasonable norm. We will further discuss the decay rate of the -th derivative with respect to the stochastic variable of the solutions. Our strategy is based on Lyapunov's method. The matrices we need for a Lyapunov's estimate now depend on the stochastic variable. This requires a careful analysis of the random effect.
Cite
@article{arxiv.2008.00322,
title = {Hypocoercivity of the linearized BGK-equation with stochastic coefficients},
author = {Tobias Herzing and Christian Klingenberg and Marlies Pirner},
journal= {arXiv preprint arXiv:2008.00322},
year = {2023}
}