报告题目：Bounded Wave Solutions to Degenerate Differential Equations
报告时间：2020年8月27日星期四，上午9:00-10.30
报告地点：腾讯会议 ID：429527366
报告人：Zhaosheng Feng 教授，School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley
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. These methods can be applied to nonlinear differential equations of an unfamiliar type and do not rely on particular tricks. In this talk, we give a straightforward introduction and applications of symmetry methods. 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