Fokker-Planck equation in bounded domain
Annales de l'Institut Fourier, Volume 60 (2010) no. 1, pp. 217-255.

We study the existence and the uniqueness of a solution ϕ to the linear Fokker-Planck equation -Δϕ+div(ϕF)=f in a bounded domain of  d when F is a “confinement” vector field. This field acting for instance like the inverse of the distance to the boundary. An illustration of the obtained results is given within the framework of fluid mechanics and polymer flows.

On étudie l’existence et l’unicité de solution ϕ à l’équation de Fokker-Planck linéaire -Δϕ+div(ϕF)=f sur un domaine borné de  d lorsque F est un champ de vecteurs “confinant” comme par exemple l’inverse de la distance au bord. Une illustration des résultats obtenus est donnée dans le cadre de la mécanique des fluides et des écoulements de polymères.

DOI: 10.5802/aif.2521
Classification: 35J25, 35Q35, 35R60, 76A05, 82D60
Keywords: Fokker-Planck equation, Bounded domain, Stationary solution, Confinement, Fluid mechanics, Polymer flows
Mot clés : équation de Fokker-Planck, domaine borné, confinement, mécanique des fluides, écoulement de polymères
Chupin, Laurent 1

1 Université de Lyon INSA de Lyon - Pôle de Mathématiques Institut Camille Jordan - UMR5208 - CNRS 21 av. Jean Capelle 69621 Villeurbanne cedex (France)
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Chupin, Laurent. Fokker-Planck equation in bounded domain. Annales de l'Institut Fourier, Volume 60 (2010) no. 1, pp. 217-255. doi : 10.5802/aif.2521. https://aif.centre-mersenne.org/articles/10.5802/aif.2521/

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