Diffusion approximation for a Knudsen gas in a thin domain with reflexive chaotic law

Abstract

This paper treats a rarefied Knudsen gas flow between two infinite plates, with boundary reflexion ruled by a reflexive chaotic law called “Arnold's cat map”. It is shown that the limiting behaviour, when the distance between the plates goes to 0, is described by an (anisotropic) diffusion equation in the norm topology.