DIFFUSION LIMITS FOR FLOWS IN THIN-LAYERS

The aim of this paper is the asymptotic behaviour of the dynamics of a test particle in a scattering medium between two parallel plates with in a small distance h of up to a few mean free paths. We prove that un der an appropriate scaling for h --> 0 (with constant ''opacity'' of t he gap, obtained by scaling up the density of the scattering medium by 1/h) a diffusion limit is obtained. The diffusion constant depends on the scattering kernel of the medium as well as on the reflection law at the walls. The proper time scaling is in all cases t/h, in contrast to results obtained for the Knudsen gas limit [C. Borgers, C. Greenga rd, and E. Thomann, SIAM J. Appl. Math., 52 (1992), pp. 1057-1075].