Longtime behavior for solutions to a temporally discrete diffusion equation with a free boundary


主讲人:郭志明 广州大学教授


地点:腾讯会议 954 594 836


主讲人介绍:郭志明,广州大学数学与信息科学学院二级教授、博士生导师。2001年博士毕业于中山大学,2009年在加拿大西安大略大学访问一年。多年来一直从事离散系统、泛函微分方程及生物数学模型的理论与应用研究,在JDE、J. London Math. Soc.、JDDE、JMB、《中国科学》等国际国内重要刊物上发表论文80多篇,其中SCI收录60多篇。先后主持国家自然科学基金面上项目4项、参加国家自然科学基金重点项目1项。获得2021年度广东省自然科学奖一等奖。

内容介绍:In this talk, we will investigate the longtime behavior of solutions to a temporally discrete diffusion equation with a fixed boundary and a free boundary respectively in one space dimension. Such equation can be equivalent in any case to an integro-difference equation, another important time discrete equation that provides powerful tools for the study of dispersal phenomena. We first discuss the global dynamics of the equation in a fixed bounded domain. With a Stefan type free boundary, we then give a new well-posedness proof and the regular spreading-vanishing dichotomy for the corresponding problem. Moreover, a modified comparison principle for the time discrete free boundary problem is proved in an effort to provide the sufficient conditions for dichotomy. It is the first attempt to study the temporally discrete diffusive phenomenon with a free boundary.