Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate

Shuichi Kawashima*, Tohru Nakamura, Shinya Nishibata, Peicheng Zhu

*この研究の対応する著者

研究成果: Article査読

35 被引用数 (Scopus)

抄録

The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence rate of solutions toward a corresponding stationary solution. Here the existence of the stationary solution is proved under a smallness condition on the boundary data with the aid of center manifold theory. We also show the time asymptotic stability of the stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. The proof is based on deriving a priori estimates by using a time and space weighted energy method.

本文言語English
ページ(範囲)2201-2235
ページ数35
ジャーナルMathematical Models and Methods in Applied Sciences
20
12
DOI
出版ステータスPublished - 2010 12月
外部発表はい

ASJC Scopus subject areas

  • モデリングとシミュレーション
  • 応用数学

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