Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition
Bernou, Armand; Carrapatoso, Kleber; Mischler, Stéphane; Tristani, Isabelle (2021), Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition. https://basepub.dauphine.psl.eu/handle/123456789/22157
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-03142785
Series titleCahier de recherche du CEREMADE
MetadataShow full item record
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Centre de Mathématiques Laurent Schwartz [CMLS]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Département de Mathématiques et Applications - ENS Paris [DMA]
Abstract (EN)We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary condition. Our proof consists in establishing an hypocoercivity result for the associated operator, in other words, we exhibit a convenient Hilbert norm for which the associated operator is coercive in the orthogonal of the global conservation laws. Our approach allows us to treat general domains with all type of boundary conditions in a unified framework. In particular, our result includes the case of vanishing accommodation coefficient and thus the specific case of the specular reflection boundary condition.
Showing items related by title and author.
Special modes and hypocoercivity for linear kinetic equations with several conservation laws and a confining potential Carrapatoso, Kleber; Dolbeault, Jean; Hérau, Frédéric; Mischler, Stéphane; Mouhot, Clément; Schmeiser, Christian (2021) Document de travail / Working paper