题目：Two species nonlocal diffusion systems with free boundaries

主讲人： 赵孟博士

时 间：2022年5月15日（星期天）晚上19：30

地 点：腾讯会议（会议号228-332-184）

主办单位：理学院

主讲人简介：

赵孟，博士，西北师范大学数学与统计学院硕士生导师。博士毕业于兰州大学应用数学专业，导师为李万同教授。主要从事自由边界问题传播动力学的学习和研究。目前主持博士后面上基金1项，在JDE、JDDE、DCDSA、ZAMP、DCDSB、CPAA等杂志上发表论文多篇。

摘要:

We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the species, but here the population dispersal is described by “nonlocal diffusion” instead of “local diffusion”. We prove that such a nonlocal diffusion problem with free boundary has a unique global solution, and for models with Lotka-Volterra type competition or predator-prey growth terms, we show that a spreading-vanishing dichotomy holds, and obtain criteria for spreading and vanishing; moreover, for the weak competition case and for the weak predation case, we can determine the long-time asymptotic limit of the solution when spreading happens. Compared with the single species free boundary model with nonlocal diffusion considered recently by Cao et.al., and the two species cases with local diffusion extensively studied in the literature, the situation considered in this paper involves several new difficulties, which are overcome by the use of some new techniques.