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Stationary Boltzmann's equation with Maxwell's boundary conditions in a bounded domain

✍ Scribed by Andrzej Palczewski

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
764 KB
Volume
15
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The paper deals with the stationary Boltzmann equation in a bounded convex domain Ω. The boundary ∂Ω is assumed to be a piecewise algebraic variety of the C^2^‐class that fulfils Liapunov's conditions. On the boundary we impose the so‐called Maxwell boundary conditions, that is a convex combination of specular and diffusive reflections. The non‐linear Boltzmann equation is considered with additional volume and boundary source terms and it has been proved that for sufficiently small sources the problem possesses a unique solution in a properly chosen subspace of C(Ω × ℝ^3^). The proof is a refined version of the proof delivered by Guiraud for purely diffusive reflection.

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