503 RWTH Publication No: 787779        2020        IGPM503.pdf
TITLE Hypocoercivity of stochastic Galerkin formulations for stabilization of kinetic equations
AUTHORS Stephan Gerster, Michael Herty, Hui Yu
ABSTRACT We employ the framework of hypocoercivity for linear kinetic equations by [18] to analyze boundary stabilization problems. In particular, we also consider relaxation approximations and their limiting behavior under boundary stabilization. Applications to the two-velocity BGK models and the linear Maxwell-Cattaneo relaxation models are studied. Further, we introduce a weaker stabilization concept based on an averaged L2-norm. In this framework, regularity results of the solution with respect to the relaxation parameter are established. Stable numerical discretizations are implemented to demonstrate also numerically the boundary stabilization and to show the expected exponential convergence to equilibria.
KEYWORDS systems of kinetic and hyperbolic balance laws, exponential stability, asymptotic stability, feedback stabilization
DOI 10.4310/CMS.2021.v19.n3.a10
PUBLICATION Communications in Mathematical Sciences, Volume 19, Issue 3 (2021), pp. 787–806