題目：Lie Symmetry Methods to DegenerateDifferential Equations
主講人：Dr. Zhaosheng Feng (美國德克薩斯大學必一体育平台數學系終身教授)
時間與地點: 6月8日15:30-17:00必一体育平台二樓會議室
摘要: There are manywell-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 Liesymmetry reduction method. For a higher-order ODE, a correspondence betweenfirst integrals and invariance under point symmetries holds only when the ODEhas a variational principle. If a system of PDEs is invariant under a Lie groupof point transformations, one can find, constructively, special solutions,called similarity solutions or invariant solutions that are invariant under asubgroup of the full group admitted by the system. We will illustrate thesetechniques to investigate a degenerate parabolic system which arises inbiological population, and obtain bounded wave solutions under certainconditions.
馮兆生博士，現在美國德克薩斯大學(University ofTexas-Rio Grande Valley)必一体育平台數學系終身教授。主要研究方向有非線性微分方程, 動力系統, 數學物理問題, 應用分析和生物數學等。目前在國際期刊上發表學術論文近140篇，其中SCI檢索近120篇，編輯出版4本英文著作，曾任第五屆國際動力系統及微分方程學術大會組委會主席，目前任5個國際雜誌的編委。