Diffusion limit for a stochastic kinetic problem

Arnaud Debussche (1, 2) , Julien Vovelle (3)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 ICJ - Institut Camille Jordan

We study the limit of a kinetic evolution equation involving a small parameter and perturbed by a smooth random term which also involves the small parameter. Generalizing the classical method of perturbed test functions, we show the convergence to the solution of a stochastic diffusion equation.

Mots clés: Kinetic equation; Diffusion limit; Stochastic equation

Domaines: Equations aux dérivées partielles [math.AP]

Arnaud Debussche, Julien Vovelle. Diffusion limit for a stochastic kinetic problem. Communications on Pure and Applied Mathematics, 2012, 11 (6), pp.2305-2326. ⟨10.3934/cpaa.2012.11.2305⟩. ⟨hal-00576610v2⟩