Fokker-Planck equation in bounded domain

Laurent Chupin[1]

  • [1] Université de Lyon INSA de Lyon - Pôle de Mathématiques Institut Camille Jordan - UMR5208 - CNRS 21 av. Jean Capelle 69621 Villeurbanne cedex (France)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 1, page 217-255
  • ISSN: 0373-0956

Abstract

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We study the existence and the uniqueness of a solution  ϕ to the linear Fokker-Planck equation - Δ ϕ + div ( ϕ F ) = f in a bounded domain of  ℝ 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.

How to cite

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Chupin, Laurent. "Fokker-Planck equation in bounded domain." Annales de l’institut Fourier 60.1 (2010): 217-255. <http://eudml.org/doc/116267>.

@article{Chupin2010,
abstract = {We study the existence and the uniqueness of a solution $\varphi $ to the linear Fokker-Planck equation $-\Delta \varphi + \operatorname\{div\}(\varphi \, \{\mathbf\{F\}\}) = f$ in a bounded domain of $\mathbb\{R\}^d$ when $\mathbf\{F\}$ 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.},
affiliation = {Université de Lyon INSA de Lyon - Pôle de Mathématiques Institut Camille Jordan - UMR5208 - CNRS 21 av. Jean Capelle 69621 Villeurbanne cedex (France)},
author = {Chupin, Laurent},
journal = {Annales de l’institut Fourier},
keywords = {Fokker-Planck equation; Bounded domain; Stationary solution; Confinement; Fluid mechanics; Polymer flows; bounded domain; stationary solution; confinement; fluid mechanics; polymer flows},
language = {eng},
number = {1},
pages = {217-255},
publisher = {Association des Annales de l’institut Fourier},
title = {Fokker-Planck equation in bounded domain},
url = {http://eudml.org/doc/116267},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Chupin, Laurent
TI - Fokker-Planck equation in bounded domain
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 1
SP - 217
EP - 255
AB - We study the existence and the uniqueness of a solution $\varphi $ to the linear Fokker-Planck equation $-\Delta \varphi + \operatorname{div}(\varphi \, {\mathbf{F}}) = f$ in a bounded domain of $\mathbb{R}^d$ when $\mathbf{F}$ 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.
LA - eng
KW - Fokker-Planck equation; Bounded domain; Stationary solution; Confinement; Fluid mechanics; Polymer flows; bounded domain; stationary solution; confinement; fluid mechanics; polymer flows
UR - http://eudml.org/doc/116267
ER -

References

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