The linear Boltzmann equation describing electron flow in a semiconductor is considered. The Cauchy problem for space-independent solutions is investigated, and without requiring a bounded collision frequency the existence of integrable solutions is established. Mass conservation, an H-theorem, and
Stationary solutions of the linearized Boltzmann equation in a half-space
โ Scribed by F. Golse; F. Poupaud; H. Neunzert
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 743 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
โฆ Synopsis
Communicated by H. Neunzert
Stationary half-space solutions of the linearized Boltzmann equation are studied by energy estimates methods. We extend the results of Bardos, Caflisch and Nicolaenko for a gas of hard spheres to a general potential. Asymptotic behaviour is obtained for hard as well as soft potentials and compared to the case of hard spheres.
๐ 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
In semiconductors the distributions of electrons satisfy a non-linear Boltzmann-Vlasov equation. We consider the half-space problem arising in the study of boundary layers when the mean free path tends to zero. We prove the existence and the uniqueness of the solution for any prescribed entering dis
## Communicated by V. Lvov Approximate solutions of the non-linear Boltzmann equation, which have the structure of the linear combination of three global Maxwellians with arbitrary hydrodynamical parameters, are considered. Some sufficient conditions which allow the error between the left-and the