Nonlinear Fokker-Planck equation with reflecting boundary conditions

Ioana Ciotir (1) , Rim Fayad (1)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

We study the existence and uniqueness of a mild solution to a nonlinear Fokker-Planck equation with reflecting boundary conditions, by using a monotonicity approach. Then we prove that the mild solution is also a distributional one.

Mots clés: Fokker-Planck equation; m-accretive operator; mild solution; McKean-Vlasov stochastic differential equation AMS [2020] Primary 60H30; 60H10; 60G46; secondary 35Q84; 35D99

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Ioana Ciotir, Rim Fayad. Nonlinear Fokker-Planck equation with reflecting boundary conditions. 2021. ⟨hal-03151286⟩