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Hypocoercivity of linear kinetic equations via Harris's Theorem

Cañizo, José; Cao, Chuqi; Evans, Josephine; Yoldaş, Havva (2020), Hypocoercivity of linear kinetic equations via Harris's Theorem, Kinetic & Related Models, 13, 1, p. 97-128. 10.3934/krm.2020004

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2019-01-23-kinetic_Harris.pdf (460.2Kb)
Type
Article accepté pour publication ou publié
Date
2020
Journal name
Kinetic & Related Models
Volume
13
Number
1
Publisher
AIMS - American Institute of Mathematical Sciences
Published in
Paris
Pages
97-128
Publication identifier
10.3934/krm.2020004
Metadata
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Author(s)
Cañizo, José
Departamento de Matemática Aplicada
Cao, Chuqi
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Evans, Josephine
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Yoldaş, Havva
Basque Center for Applied Mathematics [BCAM]
Abstract (EN)
We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus (x, v) ∈ T d × R d or on the whole space (x, v) ∈ R d × R d with a confining potential. We present explicit convergence results in total variation or weighted total variation norms (alternatively L 1 or weighted L 1 norms). The convergence rates are exponential when the equations are posed on the torus, or with a confining potential growing at least quadratically at infinity. Moreover, we give algebraic convergence rates when subquadratic potentials considered. We use a method from the theory of Markov processes known as Harris's Theorem.
Subjects / Keywords
Harris's Theorem; linear BGK

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