Fokker-Planck equation in bounded domain

Laurent Chupin (1)

1 ICJ - Institut Camille Jordan

We study the existence and the uniqueness of a solution~$\fy$ to the linear Fokker-Planck equation $-\Delta \fy + \div(\fy \, \F) = f$ in a bounded domain of $\R^d$ when $\F$ is a ``confinement'' vector 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.

Mots clés: Fokker-Planck equation; Bounded domain; Stationary solution; Confinement; Fluid mechanics; Polymer flows

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Laurent Chupin. Fokker-Planck equation in bounded domain. 2009. ⟨hal-00375802⟩