Traveling Waves and Global Stability to Time-Delayed Reaction-Diffusion Equations with Degenerate Diffusion-数学与统计学院网站

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Traveling Waves and Global Stability to Time-Delayed Reaction-Diffusion Equations with Degenerate Diffusion
作者:    时间:2018-08-08 浏览次数:

  

报告人:   梅茗教授

单  位:  麦吉尔大学

讲学时间: 2018年8月9日上午:9:00-10:00

讲学地点: 数学院一楼报告厅

拟参加人员: 相关教师和相关专业研究生

摘 要:  This talk is concerned with time-delayed reaction-diffusion equations with degenerate diffusion. When the term for birth rate is a nonlocal integral with a heat kernel, the family of minimum wave speeds corresponding to all the degenerate diffusion coefficients is proved to admit a uniform positive infimum. However, when the term for birth rate is local, there is no positive infimum of all the minimum wave speeds. This difference indicates that the nonlocal effect plays a role as Laplacian  such that a positive lower bound independent of the degenerate diffusion

exists for the minimum wave speeds.We further prove the global stability of the traveling waves. The approach adopted for the proof is the monotone technique with the viscosity vanishing method, and the technical weighted method. The degeneracy of diffusion for the equation causes us essential difficulty in the proof. A number of numerical simulations are also carried out at the end of the paper, which further numerically confirm our theoretical results.


This talk is based on two recent papers joint with Rui Huang, Shanming Ji, Chunhua Jin, Tianyuan Xu, and Jingxue Yin.