Fokker-Planck equation in bounded domain  [ Equation de Fokker-Planck dans un domaine borné ]
Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 217-255.

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.

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.

DOI : https://doi.org/10.5802/aif.2521
Classification : 35J25,  35Q35,  35R60,  76A05,  82D60
Mots clés : équation de Fokker-Planck, domaine borné, confinement, mécanique des fluides, écoulement de polymères
@article{AIF_2010__60_1_217_0,
     author = {Chupin, Laurent},
     title = {Fokker-Planck equation in bounded domain},
     journal = {Annales de l'Institut Fourier},
     pages = {217--255},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {1},
     year = {2010},
     doi = {10.5802/aif.2521},
     mrnumber = {2664314},
     zbl = {1200.35305},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_1_217_0/}
}
Chupin, Laurent. Fokker-Planck equation in bounded domain. Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 217-255. doi : 10.5802/aif.2521. http://www.numdam.org/item/AIF_2010__60_1_217_0/

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