HETEROGENEOUS DISCRETE KINETIC MODEL AND ITS DIFFUSION LIMIT

Abstract

A revertible discrete velocity kinetic model is introduced when the environment is spatially heterogeneous. It is proved that the parabolic scale singular limit of the model exists and satisfies a new heterogeneous diffusion equation that depends on the diffusivity and the turning frequency together. An energy functional is introduced which takes into account spatial hetero-geneity in the velocity field. The monotonicity of the energy functional is the key to obtain uniform estimates needed for the weak convergence proof. The Div-Curl lemma completes the strong convergence proof.