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

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arxiv 2406.10112 v2 pith:OMRAJITE submitted 2024-06-14 math.AP

Kleber Carrapatoso , Stéphane Mischler This is my paper · ORCID
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keywords equationassociateddomainfokker-planckhypocoercivitykineticultracontractivityasymptotic
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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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  1. Existence and stability of non-equilibrium steady states of a weakly non-linear kinetic Fokker-Planck equation in a domain

    math.AP 2025-06 conditional novelty 6.0 of 10

    For small values of the nonlinear parameter alpha, a kinetic Fokker-Planck equation with BGK thermostats and space-dependent Maxwell boundary conditions admits an exponentially stable non-equilibrium steady state.

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