Propagation Dynamics of Reaction and Diffusion Equations in a Time-heterogeneous Shifting Environmen

主講人：趙曉強(qiáng) 加拿大紐芬蘭紀(jì)念大學(xué)教授

時(shí)間：2023年6月19日10：00

地點(diǎn)：三號(hào)樓126室

舉辦單位：數(shù)理學(xué)院

主講人介紹：趙曉強(qiáng)，加拿大紐芬蘭紀(jì)念大學(xué)數(shù)學(xué)與統(tǒng)計(jì)系教授，該校University Research Professorship榮譽(yù)獲得者。趙教授先后于1983年和1986年在西北大學(xué)數(shù)學(xué)系獲學(xué)士和碩士學(xué)位，1990年在中國(guó)科學(xué)院應(yīng)用數(shù)學(xué)研究所獲博士學(xué)位。趙教授長(zhǎng)期從事動(dòng)力系統(tǒng)、微分方程和生物數(shù)學(xué)相關(guān)領(lǐng)域的研究，在單調(diào)動(dòng)力學(xué)、一致持久性、行波解和漸近傳播速度、基本再生數(shù)的理論及應(yīng)用等方面的系列工作受到同行的廣泛關(guān)注和引用。迄今為止，他已在“Comm. Pure Appl. Math.、 J. Eur. Math. Soc.、 J. reine angew. Math.、 J. Math. Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math. Anal.”等國(guó)際知名期刊上發(fā)表論文180余篇，并在Springer出版專著“Dynamical Systems in Population Biology”。

內(nèi)容介紹：In this talk, I will report our recent research on the propagation dynamics of a large class of nonautonomous reaction-diffusion equations with the time-dependent shifting speed having a uniform mean c. Under the assumption that in two directions of the spatial variable there are two limiting equations with one admitting a spreading speed c* and the other being asymptotic to annihilation, we show that the solutions with compactly supported initial data go to zero eventually when c is less than or equal to -c*, the leftward spreading speed is -c* when c is greater than -c*, and the rightward spreading speed is c and c* when c is in the interval (-c*,c*) and c is greater than or equal to c*, respectively. We also establish the existence, uniqueness and nonexistence of the forced traveling wave in terms of the sign of c-c*.