2017年12月21日下午，美国德克萨斯大学的冯兆生教授在学院会议室为我院教师做了题为《Lie Symmetry Methods to Degenerate Differential Equations》的讲座。讲座内容为：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。

       期间林丽珊、周正以及司新老师也汇报了自己的科研成果并就一些问题向冯教授进行请教，均得到了满意的答复。最后，参会的教师就讲座中的一些问题与冯教授进行了深入的沟通，冯教授对这些问题进行了一一解释，给所有参与讲座的老师带来了很大的收获。