Convergence to equilibrium for Fokker-Planck equation with a general force field

Mamadou Ndao (1, 2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 Université Paris-Saclay

The aim of this paper is to study the convergence of the solution of the Fokker-Planck equation to the associated stationary state when time goes to infinity. The force field which we consider here is of a general structure, that is it may not derive from a potential. The proof is based on an adequate splitting L = B+A of the Fokker-Planck operator L and the use of Krein-Rutmann theory.

Mots clés: asymptotic convergence; Krein-Rutman theorem; m-dissipative; linear operators; Fokker-Planck equation; Semigroup

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

Mamadou Ndao. Convergence to equilibrium for Fokker-Planck equation with a general force field. 2016. ⟨hal-01289188v1⟩