%0 Journal Article
%T 非齐次Burgers方程的黎曼初值扰动问题解的渐近稳定性<br>Asymptotic Stability of Shock Waves and Rarefaction Waves under Periodic Perturbations  for  Inhomogeneous  Burgers Equation
%A 张兆祥
%A 李悦
%J Pure Mathematics
%P 1400-1415
%@ 2160-7605
%D 2021
%I Hans Publishing
%R 10.12677/PM.2021.117157
%X <div style=\"text-align:justify;\">
	本文主要研究非齐次 Burgers 方程的柯西问题，初值为黎曼初值周期扰动时，基本波结构的渐近 稳定性。我们发现激波解扰动后，在有限时间 T 后仍为激波解，在任意时刻 t &gt; T ，它左右状态仍 为周期函数，且在 L<sup>∞</sup> 范数的意义下衰减至0。 特别地，扰动后的激波在原激波两侧摆动，扰动后 的稀疏波解在 L<sup>∞</sup> 范数的意义下衰减至0。<br />
In this paper we study large time behaviors toward shock waves and rarefaction waves under periodic perturbations for inhomogeneous Burgers equation. We show that for shock waves, after a finite time, the perturbed shock actually consists of two periodic functions contacting each other at a shock, and this shock curve oscillates on both sides of the background shock curve. Both of perturbed shock waves and perturbed rarefaction waves tend to zero in the L<sup>∞</sup> norm.
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%K 非齐次Burgers方程，激波，稀疏波，周期扰动，广义特征线<br>Inhomogeneous Burgers Equation
%K Shock Waves
%K Rarefaction Waves
%K Periodic Perturbations
%K Generalized Characteristics
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=44035