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题目:Lie Symmetry Methods to Degenerate Differential Equations时间:2015年12月8日(周二)下午15:00 -16:00地点:北航数学与系统科学ag平台app下载主 321学术交流厅 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. 冯兆生教授概况:: 冯兆生,男,我校杰出校友,现在美国德克萨斯大学(University of Texas-Rio Grande Valley)理ag平台app下载数学系任终身教授、博导,主要研究方向有非线性微分方程, 动力系统, 数学物理问题, 应用分析和生物数学等。目前在美国、英国、德国等国家的数学、物理和控制工程学术刊物上共发表学术论文130余篇(不含国际会议论文), 其中被SCI/SCI-E检索的论文110余篇。近年在北美出版编辑五本英文著作/论文集,曾任第五届国际动力系统及微分方程学术大会组委会主席,目前任五个国际杂志的编委。2015年5月1日获得美国德克萨斯大学年度杰出成就奖。

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