Diffusion approximation for a Knudsen gas in a thin domain with accommodation on the boundary

Article type: Research Article

Authors: Babovsky, Hans^; | Bardos, Claude | Platkowski, Tadeusz

Affiliations: FB Mathematik, University of Kaiserslautern, Postfach 3049 D–6750 Kaiserlautern, FRG | University of Paris VII, 2 Place Jussieu, 7500 Paris, France | Department of Mathematics, Informatics and Mechanics, University of Warsaw, 00–901 Warsaw, Poland

Note: [] This work was completed while the three authors were visiting the Mathematical Sciences Institute of Cornell University and they wish to thank the MSI for the corresponding support.

Abstract: 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.

DOI: 10.3233/ASY-1991-3401

Journal: Asymptotic Analysis, vol. 3, no. 4, pp. 265-289, 1991