On linear hypocoercive BGK models
Analysis of PDEs
2023-08-21 v2
Abstract
We study hypocoercivity for a class of linear and linearized BGK models for discrete and continuous phase spaces. We develop methods for constructing entropy functionals that prove exponential rates of relaxation to equilibrium. Our strategies are based on the entropy and spectral methods, adapting Lyapunov's direct method (even for "infinite matrices" appearing for continuous phase spaces) to construct appropriate entropy functionals. Finally, we also prove local asymptotic stability of a nonlinear BGK model.
Cite
@article{arxiv.1510.02290,
title = {On linear hypocoercive BGK models},
author = {Franz Achleitner and Anton Arnold and Eric A. Carlen},
journal= {arXiv preprint arXiv:1510.02290},
year = {2023}
}