报告题目：Lie Symmetry Methods to Degenerate Differential Equations

报告人：Zhaosheng Feng，  University of Texas-Rio Grande Valley

时间：12月16日（周三）下午 4:00-5:00

地点：管研楼1518

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.