云亭数学讲坛2021第54讲—李骥教授

文章来源:数学与统计学院发布日期:2021-09-26浏览次数:10

应西北师范大学数学与统计学院邀请,华中科技大学李教授将为我院师生作线上学术报告。

报告题目:Orbital Stability of the Sum of Smooth Solitons to the Degasperis- Procesi Equation

报告摘要:The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the L2 ∩ L∞ orbital stability of a wave train containing N smooth solitons which are well separated. The main difficulties stem from the subtle nonlocal structure of the DP equation. One consequence is that the energy space of the DE equation based on the conserved quantity induced by the translation symmetry is only equivalent to the L2 -norm, which by itself can not bound the higher-order nonlinear terms in the Lagrangian. Our remedy is to introduce a priori estimates based on certain smooth initial conditions. Moreover, another consequence is that the nonlocal structure of the DP equation signifificantly complicates the verification of the monotonicity of local momentum and the positive definiteness of a refifined quadratic form of the orthogonalized perturbation.

报告时间:20219288:30

报告地点:腾讯会议(ID755 622 884)

邀请人:陈鹏玉 副教授

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【报告人简介】

 李骥,华中科技大学数学与统计学院教授,博士生导师,国家级青年人才项目获得者。2008年本科毕业于南开大学数学试点班,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。主要研究随机动力系统,随机不变流形几何奇异摄动理论及应用和相应的随机扰动理论以及浅水波孤立子稳定性问题。在包括TAMS , JMPAJFAJDEDCDS, PhyDAnnPDE等杂志发表高水平学术论文二十多篇。