STATIONARY WAVES TO VISCOUS HEAT-CONDUCTIVE GASES IN HALF-SPACE: EXISTENCE, STABILITY AND CONVERGENCE RATE

DOI DOI HANDLE Web Site 被引用文献7件 参考文献14件 オープンアクセス
  • SHUICHI KAWASHIMA
    Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan
  • TOHRU NAKAMURA
    Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan
  • SHINYA NISHIBATA
    Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
  • PEICHENG ZHU
    Basque Center for Applied Mathematics (BCAM), Building 500, Bizkaia Technology Park, E-48160 Derio, Spain

書誌事項

公開日
2010-12
資源種別
journal article
DOI
  • 10.1142/s0218202510004908
  • 10.48550/arxiv.0912.4839
公開者
World Scientific Pub Co Pte Ltd

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説明

<jats:p> 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. </jats:p>

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