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Stationary Boltzmann's equation with Maxwell's boundary conditions in a bounded domain
Author(s) -
Palczewski Andrzej
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150602
Subject(s) - mathematics , boltzmann equation , boundary (topology) , mathematical analysis , bounded function , domain (mathematical analysis) , specular reflection , boundary value problem , regular polygon , reflection (computer programming) , piecewise , boltzmann constant , geometry , physics , quantum mechanics , computer science , thermodynamics , programming language
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.