Determining spreading speeds for abstract time-periodic monotone semiflows

報(bào)告題目：Determining spreading speeds for abstract time-periodic monotone semiflows

報(bào)告人：歐春華 教授 加拿大紐芬蘭紀(jì)念大學(xué)

邀請(qǐng)人：王烽

報(bào)告時(shí)間：2024年5月30日（周四）11:00-12:00

報(bào)告地點(diǎn)：南校區(qū)會(huì)議中心112會(huì)議室

報(bào)告人簡(jiǎn)介：歐春華教授1989年本科畢業(yè)于北京大學(xué)，2003年獲得香港城市大學(xué)數(shù)學(xué)博士學(xué)位。2015年至今任紐芬蘭紀(jì)念大學(xué)終身教授，博士生導(dǎo)師，主要致力于微分方程和動(dòng)力系統(tǒng)，漸近分析及工業(yè)應(yīng)用數(shù)學(xué)等方面的學(xué)術(shù)研究。歐春華教授已經(jīng)在SIAM J. Math. Anal., SIAM J.Appl. Math., SIAM J. Appl. Dyn. Syst., J. Nonlinear Sci., Nonlinearity, JDE等國(guó)際權(quán)威期刊發(fā)表了一系列高水平的學(xué)術(shù)論文，受到了國(guó)內(nèi)外同行的關(guān)注與大量引用，并且連續(xù)多年獲得加拿大國(guó)家自然科學(xué)基金及紐芬蘭省科學(xué)發(fā)展基金的支持。

報(bào)告摘要：This talk is devoted to studying the spreading speed determinacy to an abstract time-periodic monotone semiflow, which is of monostable type with weak compactness and admits boundary equilibria in the phase space. The problem is challenging due to the existence of single spreading speed or multiple spreading speeds (fastest and slowest spreading speeds). We first study under what condition single spreading speed exists and establish necessary and sufficient conditions for linear and nonlinear selections of the spreading speed as well as the minimal wave speed of traveling wavefronts. In the case of multiple spreading speeds, the determinacy of each speed is further investigated based on the connection of wavefronts to the boundary equilibria. We apply our results to four time-periodic models: a delayed diffusive equation, a stream population model with a benthic zone, a nonlocal dispersal Lotka-Volterra model, and cooperative systems.