学术讲座：Lie Symmetry Methods to Degenerate Differential Equations
时间：2017年12月22日14:30 – 15:30
地点：旗山校区理工北楼601报告厅
主讲：德克萨斯大学冯兆生教授
主办：数学与信息学院、福建省分析数学及应用重点实验室、数学研究中心
专家简介：冯兆生，美国德克萨斯大学大河谷分校(University of Texas-Rio Grande Valley)理学院数学系任终身教授、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。目前在美国、英国、德国等国家的数学、物理和控制工程学术刊物上共发表学术论文150余篇。近年在北美出版编辑六本英文著作/论文集，自1999年起应邀在四十多个国际和美国国内数学大会上作过邀请报告并参与组织多个国际学术会议，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。目前任六个国际SCI杂志的编委。
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.
