Time-Asymptotic Behavior of Wave Propagation Around a Viscous Shock Profile
Time-Asymptotic Behavior of Wave Propagation Around a Viscous Shock Profile
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DOI：
10.1007/s00220-009-0820-6
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发表时间：
2009-05
影响因子：
2.4
通讯作者：
Tai-Ping Liu;Yanni Zeng
中科院分区：
文献类型：
--
作者：
Tai-Ping Liu;Yanni Zeng
我们研究粘性守恒定律的冲击波的非线性稳定性。我们的方法基于围绕冲击曲线的线性化系统的基本解决方案的新构造。我们首次获得了冲击波上非线性波相互作用的逐点估计。我们的结果适用于所有范围的弱冲击波和小扰动。特别是，我们的结果简化为恒定状态扰动的时间渐近行为，均匀地随着冲击波的强度趋于零。
We study the nonlinear stability of shock waves for viscous conservation laws. Our approach is based on a new construction of a fundamental solution for a linearized system around a shock profile. We obtain, for the first time, the pointwise estimates of nonlinear wave interactions across a shock wave. Our results apply to all ranges of weak shock waves and small perturbations. In particular, our results reduce to the time-asymptotic behavior of constant state perturbation, uniformly as the strength of the shock wave tends to zero.