Diffusive limits for the Knudsen gas in a thin channel with accommodation on the boundary

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Abstract

We consider a model for a free molecular flow in a thin channel bounded by two parallel plates on which Maxwellian boundary conditions with (fixed) accommodation and a generic scattering kernel apply. Using functional analytic tools, we show that as the width of the channel vanishes, and on a suitable temporal scale, the evolution of the density is described by a diffusion problem. We distinguish two classes of temporal scalings (normal and anomalous) and we show that an infinitesimal amount of grazing collisions with the walls of the channel is responsible for the anomalous diffusion. The method employed is adapted from the original work of F. Golse in Asymptot. Anal. 17 (1998), 1-12.
Original languageEnglish
Pages (from-to)101 - 123
Number of pages23
JournalAsymptotic Analysis
Volume64
Issue number1-2
DOIs
Publication statusPublished - 2009
Externally publishedYes

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