主講人：李驥  華中科技大學(xué)教授

時(shí)間：2021年11月19日9：00

地點(diǎn)：騰訊會(huì)議 764 888 655   密碼 123456

舉辦單位：數(shù)理學(xué)院

主講人介紹：李驥，華中科技大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，博士生導(dǎo)師，2008年本科畢業(yè)于南開(kāi)大學(xué)數(shù)學(xué)試點(diǎn)班，2012年在美國(guó)楊伯翰大學(xué)取得博士學(xué)位，后在明尼蘇達(dá)大學(xué)和密西根州立大學(xué)做博士后。主要研究幾何奇異攝動(dòng)理論及應(yīng)用，以及淺水波孤立子穩(wěn)定性問(wèn)題。在包括TAMS  , JMPA，JFA，AnnPDE，JDE，PhyD等雜志發(fā)表論文二十多篇。

內(nèi)容介紹：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.