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【北航数学论坛】Degenerate Reaction-Diffusion Systems and Applications——Professor Zhaosheng Feng
ag平台网址:2012-05-14  浏览量:

报告题目:Degenerate Reaction-Diffusion Systems and Applications

报告人:Professor Zhaosheng Feng Department of Mathematics, University of Texas—Pan American, USA报告地点:北航数学与系统科学ag平台app下载主321学术交流厅报告时间:2012年5月14日(星期一)15:00 报告摘要: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. For example, in ecology and biology the early systematic treatment of dispersion models of biological populations [Skellam (1951)] assumed random movement. There the probability that an individual which at timet= 0 is at the pointx1moves to the pointx2inthe interval of time is the same as that of moving fromx2tox1during the same time interval. On this basis the diffusion coefficient in the classical models of population dispersion appears as constant.In this talk, we study the case that some species migrate from densely populatedareas into sparsely populated areas to avoid crowding, and investigate a more generalreaction-diffusion system by considering density-dependent dispersion as a regulatorymechanism of the cyclic changes. Here the probability that an animal moves from thepointx1tox2depends on the density atx1. Under certain conditions, we apply thehigher terms in the Taylor series and the center manifold method to obtain the localbehavior around a non-hyperbolic point of co-dimension one in the phase plane, anduse the Lie symmetry reduction method to explore bounded traveling wave solutions.Numerical simulation and biological explanation are presented.报告人概况:冯兆生,1995年4月从北京航空航天大学应用数学系硕士毕业,1995年5月—1999年8月 在北京交通大学数学系任教,1998年7月-1999年5月访问日本东京大学理工部。1999年8月—2004年6月在美国德克萨斯A&M大学(Texas A&M University-College Station)理ag平台app下载数学系攻读并获博士学位。2004年8月至今一直在美国泛美德克萨斯大学(University of Texas-Pan American)理ag平台app下载数学系从事教学科研工作,2009年8月提前晋升为Tenured-Professor(终身教授)。主要研究方向有非线性微分方程,混沌动力系统,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、瑞典、加拿大、以色列等国家的数学和物理学术刊物上共发表学术论文106篇(98篇为通讯编辑),其中被SCI/SCI-E检索的论文近90篇,出版编辑英文著作三本,并主编了三个国际数学杂志(SCI)的专辑。目前担任三个国际数学杂志的编委(Associate Editor),至今已引导博士后四名。自1999年起应邀在四十多个国际和美国国内数学大会上作过邀请报告并参与组织多个国际学术会议。曾应邀担任十余个国际数学会议学术委员会和组委会的委员,2006年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。目前任中国矿业大学和北京交通大学兼职教授。

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