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


主讲人:赵晓强 加拿大纽芬兰纪念大学教授




主讲人介绍:赵晓强,加拿大纽芬兰纪念大学数学与统计系教授,该校University Research Professorship荣誉获得者。赵教授先后于1983年和1986年在西北大学数学系获学士和硕士学位,1990年在中国科学院应用数学研究所获博士学位。赵教授长期从事动力系统、微分方程和生物数学相关领域的研究,在单调动力学、一致持久性、行波解和渐近传播速度、基本再生数的理论及应用等方面的系列工作受到同行的广泛关注和引用。迄今为止,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.”等国际知名期刊上发表论文180余篇,并在Springer出版专著“Dynamical Systems in Population Biology”。

内容介绍: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*.