讲座题目：Stability of peakons of the shallow water modeling with cubic nonlinearity

报告时间：2019年6月24日（星期一）上午8:30-9:30

报告地点：数统学院会议室

主 讲 人：刘跃 教授

讲座内容：

In this talk, I will start by demonstrating the underlying complexity of the physical system, and then I will discuss  possible simplifications in the "shallow water" regime along with the relevant physical phenomena. In particular, I will derive some simplified nonlocal shallow-water models with cubic nonlinearity, such as integrable Novikov and Modified Camassa-Holm-type equations. It is shown these approximating model equations possess a single peaked soliton and multi-peakon solutions. Finally I will prove the single peaked soliton is orbitally stable in the energy space.

主讲人简介：

刘跃，美国德克萨斯大学阿灵顿分校教授，1994年获布朗大学博士学位。刘跃教授是目前国际上偏微分方程研究尤其是浅水波领域的一流专家。在偏微分方程，应用分析和流体力学，可积系统与孤子理论，非线性波方程的稳定性理论、奇异性形成、局部和整体适定性等领域取得国际领先的成果。其成果发表在Comm. Pure Appl. Math., Adv. Math., Comm. Math. Phys., Arch. Ration.Mech. Anal., J. Funct. Anal., Trans. AMS《Physica D》《J. Differential Equations》《Nonlinearity》《Quart. of Appl. Math.》等国际著名刊物上。