报告题目：Lie Symmetry Methods to Degenerate Differential Equations

报告人：冯兆生 教授

报告时间：2017年12月21日下午14:30

报告地点：学院会议室

报告摘要：There are many well-known techniques for obtaining exact solutions of differential equations, but most of them are merely special cases of a few powerful symmetry methods. In this talk, we give a straightforward introduction and applications of Lie symmetry reduction method. For a higher-order ODE, a correspondence between first integrals and invariance under point symmetries holds only when the ODE has a variational principle. If a system of PDEs is invariant under a Lie group of point transformations, one can find, constructively, special solutions, called similarity solutions or invariant solutions that are invariant under a subgroup of the full group admitted by the system. We will illustrate these techniques to investigate a degenerate parabolic system which arises in biological population, and obtain bounded wave solutions under certain conditions.

报告人简介：冯兆生， 男，现在美国德克萨斯大学(University of Texas-Rio Grande Valley)数学与统计学院终身教授。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140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。

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