报告题目：ORBITAL STABILITY OF THE SUM OF SMOOTH SOLITONS TO THE DEGASPERIS-PROCESI EQUATION
时 间：2021-09-23 (星期四) 14:30 ~ 2021-09-23 (星期四) 15:30
地 点：腾讯会议（会议号：538 784 825）
主 办：数学与统计学院, 福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
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.
报告人简介：华中科技大学数学与统计学院教授，博士生导师，国家级青年人才入选者，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 , JMPA，JFA，JDE，PhyD，AnnPDE等杂志发表论文二十多篇。