Asymptotic stability of Novikov peakons
数学专题报告
报告题目(Title)：Asymptotic stability of Novikov peakons
报告人(Speaker)：连伟 博士 (Lund University, Centre for mathematical sciences)
地点(Place)：腾讯会议ID：428-464-756
时间(Time)：2023年 6 月14 日(周三), 19:00-20:00
邀请人(Inviter)：袁迪凡
报告摘要
In this talk, we will consider a quasilinear dispersive equation, i.e., the Novikov equation, and show the asymptotic stability of the peaked solitary waves. It was introduced in the modeling of the propagation of shallow water waves where waves are assumed to be of moderately large amplitude. Such a result is based on a rigidity property of Novikov solutions with some "localized" structure. Following Molinet's approach for the Camassa-Holm equation, we managed to overcome the lack of conservation of momentum densities of solutions by redesigning the localization of the total mass from the finite speed of propagation property of the momentum densities and exploring the uniform in time exponential decay property of the solutions from the localization of the H1 energy. The new ideas in it could be potentially useful in studying the asymptotic stability of peaked solitary waves to a wider class of models. This is a joint work with Ming Robin Chen, Dehua Wang and Runzhang Xu.
主讲人简介
连伟，隆德大学博士后，师从哈尔滨工程大学数学学院徐润章教授, 主要研究领域为位势井理论，非线性波分析和稳定性理论。博士期间获得校博士创新基金，国家奖学金，国家留学基金委公派留学奖学金资助，至今已在《Archive for Rational Mechanics and Analysis》, 《Journal of Differential Equations》, 《Advances in Nonlinear Analysis》, 《Nonlinear Analysis》和《中国科学数学》等期刊发表论文12篇。
