English
讲座编号：jz-yjsb-2016-y045
讲座问题：Lie symmetries to Degenerate Parabolic Systems
主 讲 人：冯兆生 教授 University of Texas-Rio Grande Valley
讲座时间：2016年06月03日（周五）下昼16:00
讲座所在：阜成路东校区一号楼241室
加入工具：理学院统计专业的研究生及青年西席
主理单位：理学院
主讲人简介：
冯兆生， 男，现在美国德克萨斯大学(University of Texas-Rio Grande Valley)理学院数学系终身教授。主要研究偏向有非线性微分方程, 动力系统, 数学物理问题, 应用剖析和生物数学等。现在在国际期刊上揭晓学术论文148篇，其中SCI检索近120篇，编辑出书4本英文著作，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，现在任5个国际杂志的编委。
主讲内容：
The history of the theory of reaction-diusion systems begins with the three famous 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 original 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 x1 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 diusion coe fficient in the classical models of population dispersion appears as constant. In this talk, we introduce the Lie symmetry reduction method and apply it to study the case that some species migrate from densely populated areas into sparsely populated areas to avoid crowding. We consider a more general parabolic 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 phase plane, and use the Lie symmetry reduction method to explore bounded traveling wave solutions.
