报告题目：Acceleration Propagation in Diffusion Phenomena

报告人：李万同教授（兰州大学）

报告时间：2022年5月6日（星期五）上午09:00-11:00

报告地点：腾讯会议ID：537 751 786

报告摘要：In this talk, we focus on the acceleration propagation in diffusion phenomena. It is well-known that the solution of a monostable nonlocal dispersal scalar equation spreads at a finite speed when the kernel is thin-tailed and propagates by accelerating when the kernel has a heavy tail (the fat-tailed). However, in such systems, we find that one species can propagate by accelerating although its dispersal kernel is thin-tailed, which is a new and interesting phenomenon. This gives us a new understanding of the cooperation relation in the spatial propagation of nonlocal dispersal cooperative systems. Furthermore, we determine the spreading speed of an epidemic model with nonlocal diffusion and free boundary and show that when spreading is successful, the asymptotic spreading speed is finite or infinite depending on whether a threshold condition is satisfied by the kernel function governing the spatial dispersal of the agents. This suggests that accelerated spreading is a rather common phenomenon for free boundary problems with nonlocal diffusion. In contrast, for the corresponding models with random diffusion, the spreading can only proceed with finite speed.

报告人简介：李万同，二级教授，博士，博士导师，兰州大学“萃英学者”二级岗位教授，中国数学会副理事长、甘肃省数学会理事长，兰州大学数学与统计学院院长、甘肃应用数学中心主任、甘肃省高校应用数学与复杂系统重点实验室主任。主要从事微分方程与动力系统领域的相关研究，在Marcel Dekker出版社《纯粹数学与应用数学专著系列》合作出版专著1部，主持国家自然科学基金重点项目1项，面上及国际合作项目6项，参加重点项目1项。主持完成的项目获甘肃省自然科学一等奖和二等奖各1次。1998年入选《甘肃省333科技人才工程第一层次》、2001年获第二届《教育部优秀青年教师奖》，并获《甘肃省优秀专家》称号、2004年获国务院颁发的政府特殊津贴并获《宝钢教育基金会优秀教师奖》、2009年入选甘肃省领军人才第一层次。先后担任国家自然科学基金杰青、重大、重点、面上、青年等项目会议评审专家及科技部国家重点研发计划会议评审专家。