报告题目：Orbital stability of the modified Camassa-Holm equation
时间：2021-04-28 (星期三) 10:00 ~ 2021-04-28 (星期三) 12:00
地点：腾讯会议（ID：758 102 919）
报告人：华中科技大学李骥教授
主办：数学与信息学院, 福建省分析数学及应用重点实验室, 数学研究中心，福建省应用数学中心（福建师范大学）
参加对象：相关研究方向的老师和研究生
报告摘要：We study the stability of smooth and peaked solitary waves to the modified Camassa-Holm equation. This quasilinear equation with cubic nonlinearity is completely integrable and arises as a model for the unidirectional propagation of shallow water waves. Based on the phase portrait analysis, we demonstrate the existence of unique localized smooth solitary-wave solution with certain range of the linear dispersive parameter. We then show orbital stability of the smooth solitary wave solution under small disturbances by means of variational methods, considering a minimization problem with an appropriate constraint. Using the variational approach with suitable conservation laws, we also establish the orbital stability of peakons in the Sobolev space H1∩W1,4 without the assumption on the positive momentum density initially. Finally we demonstrate spectral stability of such smooth solitary waves using refined spectral analysis of the linear operator corresponding to the second-order variational derivative of the local Hamiltonian.
报告人简介：李骥，华中科技大学数学与统计学院教授、博导，国家级人才计划入选者。2012年在美国杨伯翰大学取得博士学位，后在明尼苏达大学和密西根州立大学做博士后，主要研究几何奇异摄动理论及其应用以及相应的随机扰动理论，在TAMS，JDE，DCDS，JFA等杂志发表论文十余篇。