报告题目1及摘要

Degenerate Reaction-Diffusion System and Its Wave Solutions

Zhaosheng Feng

School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

The history of the theory of reaction-diffusion systems begins with the three famous works by Luther (1906), Fisher and Kolmogorov etc. (1937). Since these seminal papers much research has been carried out in an attempt to extend the original results to more complicated systems which arise in several fields. In this talk, we consider the case that some species migrate from densely populated areas into sparsely populated areas to avoid crowding and investigate a more general reaction-diffusion system by considering density-dependent dispersion as a regulatory mechanism of the cyclic changes. Here the probability that an animal moves from the point x_1 to x_2 depends on the density at x_1. We apply the Poincare theory and transforms to analyze local behaviors around a non-hyperbolic point of codimension one in the phase plane and use the Lie symmetry reduction to explore bounded wave solutions. Numerical simulations and biological explanation are presented.

报告人: Zhaosheng Feng教授

时间：2019年7月3日15点30分

地点：理学楼307会议室

报告题目2及摘要

Approximate Solutions of the KdV-Burgers-Kuramoto Equation

Zhaosheng Feng

School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

In this talk, we are concerned with approximate solutions of the KdV-Burgers-Kuramoto Equation by starting with Burgers-type equations, and then focus on the KdV-Burgers-Kuramoto equation, a partial differential equation that occupies a prominent position in describing some physical processes in motion of turbulence and other unstable process systems. By constructing the Abel operator inBanach space and the Poincare’s transformation, approximate wave solutions of the KdV-Burgers-Kuramoto equation are presented.

时间：2019年7月4日15点30分

地点：理学楼307会议室

报告人简介：

Zhaosheng Feng（冯兆生），美国德克萨斯大学大河谷分校(University of Texas Rio Grande Valley)数学与统计学院终身教授，德克萨斯大学杰出成就奖获得者。主要研究方向有非线性分析,分支和混沌理论,数学物理问题,数值计算和生物数学等。目前担任国际知名学术期刊Communications in Nonlinear Science and Numerical Simulation和Electronic Journal of Differential Equations的主编，同时担任六个国际SCI学术杂志的编委。

欢迎各位老师、同学及其他相关人员光临并参与讨论！