关于美国德克萨斯大学冯兆生教授学术报告的通知

　　 　　

　　报告题目：Lie symmetries to Degenerate Parabolic Systems

　　报告人： 冯兆生  教授

　　报告时间：2016年6月 16 日(周 四 ) 下午15:00-16:00

　　报告地点：理科楼 E518报告厅

　　报告人简介：

　　冯兆生教授，美国德克萨斯大学（University of Texas-Rio Grande Valley）72886必赢数学系终身教授、博导。主要研究方向有非线性微分方程、动力系统、数学物理问题、应用分析和生物数学等。目前在国际期刊上共发表学术论文140余篇, 其中被SCI检索近120篇。出版编辑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。目前任5个国际杂志的编委，2015年5月1日获得美国德克萨斯大学年度杰出成就奖。

　　报告简介：

　　The history of the theory of reaction-diffusion 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  fields. For example, in ecology and biology the early systematic treatment of dispersion models of biologicalpopulations [Skellam (1951)] assumed random movement. There the probability that an individual which at time t = 0 is at the point x_1 moves to the point x_2 in the interval of time t is the same as that of moving from x_2 to x_1 during the same time interval. On this basis the diffusion coefficient 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 probabi- lity that an animal moves from the point x_1 to x_2 depends on the density at x_1. Under certain conditions, we apply thehigher 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.