应数学与统计学院的邀请，美国德克萨斯大学冯兆生教授近期将访问我院，来访期间将为我院师生做学术报告：

        报告时间：6月15日下午17：00—18：00
        报告地点：理科楼202
        报告题目：Lie symmetries to Degenerate Parabolic Systems

        摘要：The history of the theory of reaction-diffusion systems beginswith the three famous works by Luther (1906), Fisher andKolmogorov etc. (1937). Since these seminal papers much researchhas been carried out in an attempt to extend the original resultsto more complicated systems which arise in several fields. Forexample, in ecology and biology the early systematic treatment ofdispersion models of biological populations [Skellam (1951)]assumed random movement. There the probability that an individualwhich at time $t=0$ is at the point $x_1$ moves to the point $x_2$in the interval of time $\Delta t$ is the same as that of movingfrom $x_2$ to $x_1$ during the same time interval. On this basisthe diffusion coefficient in the classical models of populationdispersion appears as constant.In this talk, we introduce the Lie symmetry reduction method andapply it to study the case that some species migrate fromdensely populated areas into sparsely populated areas to avoidcrowding. We consider a more general parabolic systemby considering density-dependent dispersion as a regulatorymechanism of the cyclic changes. Here the probability that ananimal moves from the point $x_1$ to $x_2$ depends on the densityat $x_1$. Under certain conditions, we apply the higher terms inthe Taylor series and the center manifold method to obtain thelocal behavior around a non-hyperbolic point of codimension one inthe phase plane, and use the Lie symmetry reduction method toexplore bounded traveling wave solutions.

        报告人简介：冯兆生博士，2004年毕业于美国Texas A&M University，获博士学位，现任美国德克萨斯大学(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。目前在国际期刊上发表学术论文近百余篇，编辑出版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。

        欢迎感兴趣的师生参加！