Diffusion approximation in heterogeneous media

Article type: Research Article

Authors: Goudon, Thierry^; | Mellet, Antoine

Affiliations: Laboratoire J.A. Dieudonné, UMR 6621, Université Nice‐Sophia Antipolis, Parc Valrose, F‐06108 Nice cedex 02, France E‐mail: [email protected] | MIP, UMR 5640, Université Paul Sabatier, 118, route de Narbonne, F‐31062 Toulouse cedex, France E‐mail: [email protected]‐tlse.fr

Note: [] Research is supported in part by INRIA‐Sophia, project CAIMAN and by the Institute for Mathematics and its Applications, University of Minnesota where this work has been achieved.

Abstract: We investigate the behaviour of the solutions of kinetic equations as a parameter related to both the mean free path and a characteristic length of heterogeneities goes to 0. We obtain in the limit a diffusion equation for the macroscopic density which combines the homogenization effects to the diffusion approximation. In particular the limit equation contains drift terms related to the behaviour of the kernel of the collision operator.

Journal: Asymptotic Analysis, vol. 28, no. 3-4, pp. 331-358, 2001