题目：Lie Symmetry Methods to DegenerateDifferential Equations
主讲人：Dr. Zhaosheng Feng (美国德克萨斯大学理学院数学系终身教授)
时间与地点: 6月8日15:30-17:00理学院二楼会议室
摘要: There are manywell-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 Liesymmetry reduction method. For a higher-order ODE, a correspondence betweenfirst integrals and invariance under point symmetries holds only when the ODEhas a variational principle. If a system of PDEs is invariant under a Lie groupof point transformations, one can find, constructively, special solutions,called similarity solutions or invariant solutions that are invariant under asubgroup of the full group admitted by the system. We will illustrate thesetechniques to investigate a degenerate parabolic system which arises inbiological population, and obtain bounded wave solutions under certainconditions.
冯兆生博士，现在美国德克萨斯大学(University ofTexas-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140篇，其中SCI检索近120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。