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Pré-Publication, Document De Travail Année : 2024

Constructive Krein-Rutman result for Kinetic Fokker-Planck equations in a domain

Résumé

We consider a general Kinetic Fokker-Planck (KFP) equation in a domain with Maxwell reflection condition on the boundary, not necessarily with conservation of mass. We establish the wellposedness in many spaces including Radon measures spaces, and in particular the existence and uniqueness of fundamental solutions. We also establish a Krein-Rutman theorem with constructive rate of convergence in an abstract setting that we use for proving that the solutions to the KFP equation converge toward the conveniently normalized first eigenfunction. Both results use the ultracontractivity of the associated semigroup in a fundamental way.
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Dates et versions

hal-04650292 , version 1 (16-07-2024)

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Kleber Carrapatoso, Pierre Gabriel, Richard Medina, Stéphane Mischler. Constructive Krein-Rutman result for Kinetic Fokker-Planck equations in a domain. 2024. ⟨hal-04650292⟩
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