Abstract
In this paper, the existence of boundary layer solutions to the Boltzmann equation for hard potential with mixed boundary condition, i.e., a linear combination of Dirichlet boundary condition and diffuse reflection boundary condition at the wall, is considered. The boundary condition is imposed on the incoming particles, and the solution is supposed to approach to a global Maxwellian in the far field. As for the problem with Dirichlet boundary condition (Chen et al., 2004 [5]), the existence of a solution highly depends on the Mach number of the far field Maxwellian. Furthermore, an implicit solvability condition on the boundary data which shows the codimension of the boundary data is related to the number of the positive characteristic speeds is also given. © 2010 Elsevier Inc.
| Original language | English |
|---|---|
| Pages (from-to) | 725-737 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 375 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Mar 2011 |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
1 The author’s research was supported both by the National Natural Science Foundation of China Grant No. 10871187, and the Natural Science Foundation of Anhui Grant No. 070416228.
Research Keywords
- Boltzmann equation
- Boundary layer
- Hard potential
- Mixed boundary condition
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