Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate
Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate
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DOI：
10.1142/s0218202510004908
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发表时间：
2009-12
影响因子：
3.5
通讯作者：
S. Kawashima;Tohru Nakamura;S. Nishibata;P. Zhu
中科院分区：
文献类型：
--
作者：
S. Kawashima;Tohru Nakamura;S. Nishibata;P. Zhu
本文主要研究一维半空间中可压缩粘性气体的理想多方模型解的大时间行为。我们考虑了一个外流问题，并得到了相应的平稳解的收敛速度。在边界数据较小的条件下，借助中心流形理论证明了稳态解的存在性。我们还证明了时间渐近稳定的定态解的边界数据和初始扰动在Sobolev空间的小假设下，通过采用能量方法。当初始扰动属于加权Sobolev空间时，得到了解向平稳解的收敛速度。证明是基于推导先验估计，通过使用时间和空间加权能量方法。
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.