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名 称 吴文俊数学重点实验室动力系统系列讲座之四十一
题 目 Lie Symmetry Methods to Degenerate Differential Equations
报告人 Zhaosheng Feng, University of Texas-Rio Grande Valley
时 间 2015-12-16 下午 4:00-5:00
地 点 管研楼1518
详 细

 

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.

 
 
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