激波对应的边界效应双曲-椭圆耦合系统平面平稳解的收敛速率

IF 2.4 2区 数学 Q1 MATHEMATICS
Shanming Ji, Minyi Zhang, Changjiang Zhu
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引用次数: 0

摘要

本文研究了半空间上辐射气体的双曲-椭圆耦合系统在u(0,y,t)=u−和u(∞,y,t)=u+<;u−条件下初边值问题解的渐近性,其中对应的Cauchy问题允许激波作为渐近轮廓。在u+<;u−≤0的情况下,假设初始扰动很小,证明了当时间趋于无穷时,问题的解收敛于相应的平面平稳解。在此基础上,利用时间和空间加权能量法得到了收敛速率。结果包括一维和二维情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Convergence rates toward the planar stationary solution for a hyperbolic-elliptic coupled system with boundary effect corresponding to shock wave
In this paper, we study the asymptotic behavior of solutions to an initial-boundary value problem for a hyperbolic-elliptic coupled system of the radiating gas on half space with the conditions u(0,y,t)=u and u(,y,t)=u+<u, where the corresponding Cauchy problem admits the shock wave as an asymptotic profile. In the case of u+<u0, we prove that the solution to the problem converges to the corresponding planar stationary solution as time tends to infinity by assuming that the initial perturbation is small. Furthermore, we obtain the convergence rate by applying the time and space weighted energy method. The results include one-dimensional and two-dimensional cases.
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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
期刊介绍: The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics
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