广义Korteweg-de Vries-Burgers方程在周期扰动下趋于稀疏波的收敛速率

中文摘要 AI 辅助

本文研究了广义Korteweg-de Vries-Burgers方程在空间周期扰动下的稀疏波。研究表明，如果稀疏波周围的初始扰动适当小，则系统的解趋于稀疏波。由于扰动在远场持续振荡，周期扰动下解的稳定性是一个有趣且重要的问题。证明的关键是构造一个携带与解相同振荡的合适拟设。然后我们可以找到解与拟设之间的抵消，使得扰动属于某个Sobolev空间。非线性稳定性可通过能量方法获得。

英文摘要

In this paper, a rarefaction wave under space-periodic perturbation for the generalized Korteweg-de Vries-Burgers equation is considered. It is shown that if the initial perturbation around the rarefaction wave is suitably small, then the solution of the system tends to the rarefaction wave. The stability of solution under periodic perturbation is an interesting and important problem since the perturbation keeps oscillating at the far fields. The key of proof is to construct a suitable ansatz carrying the same oscillation as the solution. Then we can find cancellations between solutions and ansatz such that the perturbation belongs to some Sobolev space. The nonlinear stability can be obtained by the energy method.

发表机构

• Handan University（邯郸学院）
• The Hong Kong Polytechnic University（香港理工大学）

机构由 AI 辅助整理，请以论文原文为准。