一类机制反应扩散模型中脉冲波的稳定性

主讲人：李骥  华中科技大学教授

时间：2021年11月19日9：00

地点：腾讯会议 764 888 655   密码 123456

举办单位：数理学院

主讲人介绍：李骥，华中科技大学数学与统计学院教授，博士生导师，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，以及浅水波孤立子稳定性问题。在包括TAMS  , JMPA，JFA，AnnPDE，JDE，PhyD等杂志发表论文二十多篇。

内容介绍：We analyze the stability of traveling wave in a reaction-diffusion-mechanics  system, which is derived by Holzer, Doelman and Kaper recently. This system  consists of a modified FitzHugh-Nagumo system bidirectionally coupling with an  elasticity equation. We analyze the spectrum of traveling pulse in this  reaction-diffusion-mechanics system by using geometric singular perturbation  theory and Lin-Sandstede exponential dichotomy method, and we prove that the  traveling pulse is linearly stable. Especially, we prove that there are at most  one nontrival eigenvalue near the origin, which determines the stability.  Furthermore, we provide an approximation of this eigenvalue and confirm that  it’s negative. The main tool in this paper is exponential dichotomies. We  construct piece-wise smooth candidate eigenfunction using exponential dichotomy  and then match at those jump points. From those matching condition, we solve a  useful expression for the non-trivial eigenvalue.