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Original Articles

Steady solutions of the nonlinear Boltzmann equation

Pages 257-271 | Received 03 Nov 1997, Accepted 23 Jan 1998, Published online: 20 Aug 2006
 

Abstract

We survey the problem of finding steady solutions for the Boltzmann equation. Then we present a proof that the Boltzmann equation in a slab, with boundary conditions of diffuse reflection and mass conservation at the wall and assigned total mass (per unit area) in a slab has at least one positive solution. The physical model is provided by Maxwellian molecules with angular cutoff. The equation is rewritten after a change of variables which is shown to be invertible.

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