Quantitative rates of convergence to equilibrium for the degenreate linear Boltzman equation on the Torus
Evans, Josephine; Moyano, Iván (2019-09), Quantitative rates of convergence to equilibrium for the degenreate linear Boltzman equation on the Torus. https://basepub.dauphine.fr/handle/123456789/20114
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02285239
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Statistical Laboratory [Cambridge]
Abstract (EN)We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In  Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump rate satisfies the geometric control condition of Bardos, Lebeau and Rauch . In  Han-Kwan and Léautaud showed a more general result for linear Boltzmann equations under the action of potentials in different geometric contexts, including the case of unbounded velocities. In this paper we obtain quantitative rates of convergence to equilibrium when the geometric control condition is satisfied, using a probabilistic approach based on Doeblin's theorem from Markov chains.
Subjects / KeywordsConvergence to equilibrium; Hypocoercivity; Linear Boltzmann Equation; Degenerate Hypocoercivity, Geometric Control Condition
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