ON THE EXISTENCE OF WEAK SOLUTION OF THE KINETIC FOKKER-PLANCK EQUATION IN A BOUNDED DOMAIN WITH ABSORBING BOUNDARY - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

ON THE EXISTENCE OF WEAK SOLUTION OF THE KINETIC FOKKER-PLANCK EQUATION IN A BOUNDED DOMAIN WITH ABSORBING BOUNDARY

Résumé

We study here the kinetic Fokker-Planck equation in a bounded domain with absorbing bound- ary. We show the existence and the uniqueness of a weak solution to the initial-boundary problem and we associate it to a positive compact strongly continuous semigroup. Then, we establish that the weak solution satisfies the balanced exponential growth, meaning both exponential decay toward zero and a thermalization phenomenon. Eventually, we show that it has a trace in the sense of the Green formula.
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Dates et versions

hal-04197938 , version 1 (06-09-2023)
hal-04197938 , version 2 (03-11-2023)

Identifiants

  • HAL Id : hal-04197938 , version 2

Citer

Étienne Bernard. ON THE EXISTENCE OF WEAK SOLUTION OF THE KINETIC FOKKER-PLANCK EQUATION IN A BOUNDED DOMAIN WITH ABSORBING BOUNDARY. 2023. ⟨hal-04197938v2⟩
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