Diffusion-approximation for a kinetic equation with perturbed velocity redistribution process

Nils Caillerie (1) , Julien Vovelle (2)

1 Académie de Grenoble
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the limit we obtain is a parabolic stochastic partial differential equation on the macroscopic parameter, the density here.

Mots clés: diffusion-approximation; run-and-tumble; hydrodynamic limit

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

Nils Caillerie, Julien Vovelle. Diffusion-approximation for a kinetic equation with perturbed velocity redistribution process. 2020. ⟨hal-01672879v2⟩