On Deterministic Approximation of the Boltzmann Equation in a Bounded Domain
β Scribed by Filbet, Francis
- Book ID
- 115455087
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2012
- Tongue
- English
- Weight
- 454 KB
- Volume
- 10
- Category
- Article
- ISSN
- 1540-3459
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π SIMILAR VOLUMES
A contraction mapping (or, alternatively, an implicit function theory) argument is applied in combination with the Fredholm alternative to prove the existence of a unique stationary solution of the non-linear Boltzmann equation on a bounded spatial domain under a rather general reflection law at the
Boundaries occur naturally in kinetic equations, and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: in-flow, boun
## Abstract The paper deals with the stationary Boltzmann equation in a bounded convex domain Ξ©. The boundary βΞ© is assumed to be a piecewise algebraic variety of the __C__^2^βclass that fulfils Liapunov's conditions. On the boundary we impose the soβcalled Maxwell boundary conditions, that is a co