勷勤数学•专家报告

题      目：Sharp traveling waves for degenerate diffusion equations: Spreading speed, regularity, stability

报  告  人：梅茗 教授  (邀请人：李颖花)

                                 加拿大麦吉尔大学及Champlain学院

时      间：12月20日  17：00-18：00

地     点：数科院西楼111报告厅

报告人简介:

       梅茗教授为加拿大尚布兰学院数学系的终身教授及加拿大麦吉尔大学数学与统计系的Adjunct Professor，同时也是东北师范大学的“长白山学者”讲座教授和“东师学者”讲座教授，以及日本金泽大学的合作教授。在流体力学中可压缩Navier-Stokes方程、Euler方程、Euler-Poisson方程、非线性波的稳定性、音速边界半导体动力学模型的数学分析等方面取得了系列重要的原创结果。其研究课题连续得到加拿大自然科学基金，加拿大魁北克省自然科学基金及魁北克省大专院校国际局的资助。在本领域的一流学术刊物Arch. Ration. Mech. Anal., SIAM J. Math. Anal.等发表论文 120 余篇。同时也是《Applicable Analysis》等5个SCI期刊的副主编和编委。

摘      要：

       In this talk, we focus  on time-delayed reaction-diffusion equations  with degenerate diffusion, which represent the population dynamics. First of all, we introduce  the theory related to the existence and uniqueness of traveling waves. Theses wavefronts can be sharp and loss their regularities, due to the heavy effect of degenerate diffusion. The wavefronts are also oscillating, effected by the large time delay. Secondly, we investigate the nonlinear asymptotic stability of sharp travelling waves. reaction-diffusion equations, particularly, when the time-delay is large, different from the regular reaction-diffusion equations without delay, the time-delay will cause the waves to be oscillating. In particular, we focus on the stability of traveling waves, particularly, the oscillating traveling waves. This talk is based on our 5 recent research papers joint with Shanming Ji, Tianyuan Xu and Jingxue Yin.

          欢迎老师、同学们参加、交流！