学 术 报 告

报告人：黄文璋 教授

University of Alabama in Huntsville, USA

题目1：Traveling Wave Solutions for Diffusive Predator-Prey Systems I

时间：6 月 17 日（星期三），下午 1:30-2:50

地点：致远楼102

题目2：Traveling Wave Solutions for Diffusive Predator-Prey Systems II

时间：6 月 18 日（星期四），下午 1:30-2:50

地点：致远楼102

欢迎各位老师和同学参加！

黄文璋教授在1979-1982期间就读于安徽大学数学系获硕士学位，1986-1990就读于美国Claremont研究生院获博士学位。 1990.1-1994.3先后在美国乔治亚工学院非线性动力系统中心和Cornell大学做博士后或访问教授。1994.3至今在美国阿拉巴马大学先后任助理教授，副教授和教授。黄文璋教授是北美地区在微分方程与动力系统及应用的研究领域中的最活跃的学者之一。近年来主要从事偏泛函微分方程、应用动力系统、生物生态模型和偏微分方程的行波解的研究，取得了一系列有影响的成果，在诸如J.Diff. Equns 和SIAM J. Appl. Math 等许多国际知名杂志上发表了有关SCI学术论文60余篇， 尤其在具时滞的反映扩散方程的分支理论和行波解理论研究方面做出了开创性的工作。

报告摘要

The reaction-diffusion systems, which have been frequently used as the models for many problems in physics, chemistry and biology, can give rise to an important solutions – the wave solutions. In this talk we begin with a brief introduction to the history and development of research done on the traveling waves solutions for reaction-diffusion systems, such as the shooting method, monotone iteration for monotone systems, perturbation approach, and application of Schauder’s fixed point theorem. We then present a recently developed method to study the existence of traveling wave fronts for a general class of models of predator-prey interaction described by reaction-diffusion systems. Our approach consists of a geometrical shooting argument and an analytic method by the construction of a Liapunov function and the use of Lasalle's invariance principle. Our approach can be extended to larger class of reaction-diffusion systems, such as the models of combustion, Belousov-Zhabotinskii reaction, SI-type of disease transmission, and the model of chemostat.