Existence of a stationary wave for the discrete Boltzmann equation in the half space

Shuichi Kawashima*, Shinya Nishibata

*この研究の対応する著者

研究成果: Article査読

15 被引用数 (Scopus)

抄録

We study the existence and the uniqueness of stationary solutions for discrete velocity models of the Boltzmann equation in the first half space. We obtain a sufficient condition that guarantees the existence and the uniqueness of solutions connecting the given boundary data and the Maxwellian state at a spatially asymptotic point. First, a sufficient condition is obtained for the linearized system. Then this result as well as the contraction mapping principle is applied to prove the existence theorem for the nonlinear equation. Also, we show that the stationary wave approaches the Maxwellian state exponentially at a spatially asymptotic point. We also discuss some concrete models of Boltzmann type as an application of our general theory. Here, it turns out that our sufficient condition is general enough to cover many concrete models.

本文言語English
ページ(範囲)385-409
ページ数25
ジャーナルCommunications in Mathematical Physics
207
2
DOI
出版ステータスPublished - 1999 1月 1
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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