非齐次Burgers方程的黎曼初值扰动问题解的渐近稳定性
Asymptotic Stability of Shock Waves and Rarefaction Waves under Periodic Perturbations for Inhomogeneous Burgers Equation
摘要: 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 > T ，它左右状态仍 为周期函数，且在 L∞ 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∞ 范数的意义下衰减至0。
Abstract: 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∞ norm.
文章引用：张兆祥, 李悦. 非齐次Burgers方程的黎曼初值扰动问题解的渐近稳定性[J]. 理论数学, 2021, 11(7): 1400-1415. https://doi.org/10.12677/PM.2021.117157

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