| 报告题目： | Degenerate Reaction-Diffusion Systems and Applications |
| 报 告 人： | Professor Zhaosheng Feng |
| Department of Mathematics, University of Texas-Pan American, USA | |
| 报告时间： | 6月7日上午9:30-10:30（星期四） |
| 报告地点： | 九龙湖校区数学系第一报告厅 |
| 相关介绍： | abstract: The history of the theory of reaction-di usion systems begins with the three fa-mous works by Luther (1906), Fisher and Kolmogorov etc. (1937). Since these seminal papers much research has been carried out in an attempt to extend the origi nal results to more complicated systems which arise in several elds. For example, in ecology and biology the early systematic treatment of dispersion models of biological populations [Skellam (1951)] assumed random movement. There the probability that an individual which at time t = 0 is at the point 1 moves to the point x2 in the interval of time t is the same as that of moving from x2 to x1 during the same time interval. On this basis the di usion coecient in the classical models of population dispersion appears as constant. In this talk, we study the case that some species migrate from densely populated areas into sparsely populated areas to void crowding, and investigate a more general reaction-di usion system by considering density-dependent dispersion as a regulatory mechanism of the cyclic changes. Here the probability that an animal moves from the point x1 to x2 depends on the density at x1. Under certain conditions, we apply the higher terms in the Taylor series and the center manifold method to obtain the local behavior around a non-hyperbolic point of codimension one in the pase plane, and use the Lie symmetry reduction method to explore bounded traveling wave solutions.Numerical simulation and biological explanation are presented. 冯兆生博士简介： 冯兆生， 男，现在美国泛美德克萨斯大学(University of Texas-Pan American)理学院数学系任教授。主要研究方向有非线性微分方程, 混沌动力系统, 数学物理问题, 应用分析和生物数学等。目前发表SCI/SCI-E 检索的论文近90 篇，编辑出版三本英文著作，2006 曾任第五届国际动力系统及微分方程学术大会组委会主席。 |
