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

Shuichi Kawashima, Tohru Nakamura, Shinya Nishibata, Peicheng Zhu

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2201-2235
Number of pages35
JournalMathematical Models and Methods in Applied Sciences
Volume20
Issue number12
DOIs
Publication statusPublished - 2010 Dec 1
Externally publishedYes

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Keywords

  • boundary layer solution
  • Compressible Navier-Stokes equation
  • Eulerian coordinate
  • ideal polytropic model
  • outflow problem
  • weighted energy method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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