Diffusion limit for a stochastic kinetic problem

Arnaud Debussche; Julien Vovelle

doi:10.3934/cpaa.2012.11.2305

Article Contents

2012, Volume 11, Issue 6: 2305-2326. Doi: 10.3934/cpaa.2012.11.2305

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Diffusion limit for a stochastic kinetic problem

Arnaud Debussche^1, and
Julien Vovelle^2,

1.
IRMAR and ENS de Cachan, antenne de Bretagne, Campus de Ker Lann, 35170 BRUZ Cedex
2.
Université de Lyon, CNRS UMR 5208 & Université Lyon 1, Institut Camille Jordan, 43 bd du 11 novembre 1918, F-69622 Villeurbanne cedex

Received: January 31, 2011

Revised: June 30, 2011

Published: October 2012

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Abstract

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.

Keywords:

Diffusion limit,
kinetic equations,
stochastic partial differential equations,
perturbed test functions.

Mathematics Subject Classification: Primary: 35B25, 35Q35; Secondary: 60F05, 60H15, 82C40, 82D30.

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