Diffusion approximation for a Knudsen gas in a thin domain with accommodation on the boundary
Hans Babovsky, Claude Bardos, Tadeusz Płatkowski · Asymptotic Analysis · 1991
The purpose of this work is to show how a rough boundary described by a diffusive boundary condition may generate a diffusion process in a fluid. At variance with previous results obtained by probalistic argument (cf. Babovsky (1986)), our proof relies entirely on functional analysis. It may be less intuitive but it is convenient for generalization to related phenomena. It is based on the introduction of a small parameter ε which describes the thickness of the domain compared with the effect of the boundary. Since we are aiming at a diffusion process it is also natural to introduce a scaling in time. This scaling will also be chosen of the order of 1/ε.