Diffusion approximation for a Knudsen gas in a thin domain with reflexive chaotic law
Christian Dogbé · Bulletin of the Australian Mathematical Society · 2001
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.