Convergence rates toward the travelling waves for a model system of the radiating gas
Convergence rates toward the travelling waves for a model system of the radiating gas
复制标题
DOI：
10.1002/mma.800
复制
发表时间：
2007-04
影响因子：
2.9
通讯作者：
Masataka Nishikawa;S. Nishibata
中科院分区：
文献类型：
--
作者：
Masataka Nishikawa;S. Nishibata
本文研究辐射气体模型系统解的渐进性。以前的研究表明，当时间t趋于无穷大时，解收敛到速率为（1 + t）−1/4的行波，只要初始数据由适当的Sobolev空间中的行波的小扰动给出，并且扰动是可积的。在本文中，我们做了更详细的分析，在适当的假设下的初始数据，以获得比以前的研究成形收敛速度。第一个结果是，如果初始数据在空间渐近点以一定的代数速率衰减，则该速率反映时间渐近收敛速率。准确地说，这个收敛速度与初始扰动的空间收敛速度完全相同。第二个结果是，如果初始数据由Riemann数据给定，则具有间断的容许弱解指数快速地收敛到行波。这两个结果证明了通过适当选择的权函数的能量方法获得的衰减估计的时间。版权所有© 2006约翰威利父子有限公司。
The present paper is concerned with an asymptotics of a solution to the model system of radiating gas. The previous researches have shown that the solution converges to a travelling wave with a rate (1 + t)−1/4 as time t tends to infinity provided that an initial data is given by a small perturbation from the travelling wave in the suitable Sobolev space and the perturbation is integrable. In this paper, we make more elaborate analysis under suitable assumptions on initial data in order to obtain shaper convergence rates than previous researches. The first result is that if the initial data decays at the spatial asymptotic point with a certain algebraic rate, then this rate reflects the time asymptotic convergence rate. Precisely, this convergence rate is completely same as the spatial convergence rate of the initial perturbation. The second result is that if the initial data is given by the Riemann data, an admissible weak solution, which has a discontinuity, converges to the travelling wave exponentially fast. Both of two results are proved by obtaining decay estimates in time through energy methods with suitably chosen weight functions. Copyright © 2006 John Wiley & Sons, Ltd.