Hypocoercivity of linear kinetic equations via Harris's Theorem

Abstract : 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.
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Submitted on : Monday, July 22, 2019 - 4:59:35 PM
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  • HAL Id : hal-02049210, version 2
  • ARXIV : 1902.10588

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José Cañizo, Chuqi Cao, Josephine Evans, Havva Yoldaş. Hypocoercivity of linear kinetic equations via Harris's Theorem. 2019. ⟨hal-02049210v2⟩

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