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

Shuichi Kawashima, Shinya Nishibata

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)385-409
Number of pages25
JournalCommunications in Mathematical Physics
Volume207
Issue number2
DOIs
Publication statusPublished - Jan 1 1999

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Discrete Equations
half spaces
Boltzmann Equation
Half-space
uniqueness
Sufficient Conditions
Discrete Velocity Models
existence theorems
Contraction Mapping Principle
Uniqueness of Solutions
Stationary Solutions
Ludwig Boltzmann
Existence Theorem
nonlinear equations
contraction
Nonlinear Equations
Uniqueness
Cover
Model

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Existence of a stationary wave for the discrete Boltzmann equation in the half space. / Kawashima, Shuichi; Nishibata, Shinya.

In: Communications in Mathematical Physics, Vol. 207, No. 2, 01.01.1999, p. 385-409.

Research output: Contribution to journalArticle

Kawashima, Shuichi ; Nishibata, Shinya. / Existence of a stationary wave for the discrete Boltzmann equation in the half space. In: Communications in Mathematical Physics. 1999 ; Vol. 207, No. 2. pp. 385-409.
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