报告题目：Stability of peaked solitary waves for a class of cubic quasilinear shallow-water equations            

主 讲 人：狄华斐    教授  （广州大学）    

报告时间： 2024年10月29日下午15:30-16:30          

报告地点：腾讯会议：386-146-178      

报告摘要： This talk is concerned with two classes of cubic quasilinear equations, which can be derived as asymptotic models from shallow-water approximation to the 2D incompressible Euler equations. One class of the models has homogeneous cubic nonlinearity and includes the integrable modified Camassa–Holm (mCH) equation and Novikov equation, and the other class encompasses both quadratic and cubic nonlinearities. It is demonstrated here that both these models possess localized peaked solutions. By constructing a Lyapunov function, these peaked waves are shown to be dynamically stable under small perturbations in the natural energy space H1, without restriction on the sign of the momentum density. In particular, for the homogeneous cubic nonlinear model, we are able to further incorporate a higher-order conservation law to conclude orbital stability in H1 ∩ W1,4. Our analysis is based on a strong use of the conservation laws, the introduction of certain auxiliary functions, and a refined continuity argument.      

主讲人简介: 狄华斐，博士（后），教授，2015年10月至今在广州大学数学与信息科学学院任职。2018年10月-2020年6月在The University of Texas at Arlington博士后研究合作。主要从事发展方程的定性分析、无穷维动力系统及水波理论。目前已在Int. Math. Res. Not., Physica D., J. Differ. Equations, Stud.  Appl. Math., Discrete  Cont. Dyn.,Nonlinear Anal. RWA.、Appl. Math. Lett. 等国际期刊上发表论文40余篇，主持、完成2项国家自然科学基金项目，3项广东省自然科学基金项目。