The Kinetic Fokker-Planck equation in a domain: Ultracontractivity, hypocoercivity and long-time asymptotic behavior - Département de mathématiques
Preprints, Working Papers, ... Year : 2024

The Kinetic Fokker-Planck equation in a domain: Ultracontractivity, hypocoercivity and long-time asymptotic behavior

Abstract

We consider the Kinetic Fokker-Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce the convergence with constructive rate of the solution to the KFP equation towards the stationary state with same mass as the initial datum.

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Analysis of PDEs [math.AP]
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https://hal.science/hal-04613942

Submitted on : Monday, June 17, 2024-10:59:03 AM

Last modification on : Thursday, August 1, 2024-1:48:05 PM

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hal-04613942 , version 1 (17-06-2024)

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Kleber Carrapatoso, Stéphane Mischler. The Kinetic Fokker-Planck equation in a domain: Ultracontractivity, hypocoercivity and long-time asymptotic behavior. 2024. ⟨hal-04613942⟩

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