报告题目：Free boundary problems of the diffusive Leslie-Gower model

报告人： 王明新教授（哈尔滨工业大学）

报告时间地点：2017.10.19（周四）上午10:00-11:00，理科楼407

Abstract:

In this talk we consider a free boundary problem for the Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries represent expanding fronts of the predator species. We first prove the existence, uniqueness and regularity of global solution. Then provide a spreading-vanishing dichotomy, namely the predator species either successfully spreads to infinity as $t\to\infty$ at both fronts and survives in the new environment, or it spreads within a bounded area and dies out in the long run while the prey species stabilizes at a positive equilibrium state. The criteria for spreading and vanishing are also obtained. Because the term $v/u$ (which appears in the second equation) may be unbounded when $u$ nears zero, it will bring some difficulties in the study.

王明新教授简介：   

     王明新，哈尔滨工业大学理学研究中心教授，博士生导师。河南省优秀专家称号及国务院政府特殊津贴获得者。在国内外知名期刊“J. Funct. Anal.”、“J. Differential Equations”、“J. Math. Pures Appl.”、“Nonlinearity”、“Proc. Roy. Soc. Edinburgh Sect. A”、“IMA J. Appl. Math.”等上发表论文260余篇，科学出版社出版专著5本，参与编写了科学出版社出版的“数学大辞典”，高等教育出版社出版专著1本，清华大学出版社出版教材4本。主持完成国家自然科学基金项目8项，在研1项；主持完成省部级项目8项。获得教育部科技进步奖2项，江苏省科技进步奖1项，高等学校科学研究优秀成果奖自然科学奖1项，江苏省首届青年科学家奖提名奖，河南省青年科技奖，江苏省优秀研究生指导教师，华英文化教育基金奖。

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