On the mean speed of bistable transition fronts in unbounded domains


主讲人:郭宏骏  同济大学特聘研究员




主讲人介绍:郭宏骏博士,现为同济大学数学科学学院特聘研究员,2012年于兰州大学本科毕业,2018年于法国Aix-Marseille Université  获博士学位,导师为国际知名应用数学家F. Hamel教授。郭宏骏博士的研究领域为抛物方程和广义行波解问题,在Math. Ann., J.  Math. Pures Appl., Calc. Var. Part. Differ. Equ., J. Diff.  Equations等国际期刊发表过学术论文。

内容介绍:This talk is concerned with the existence and further properties of propagation  speeds of transition fronts for bistable reaction-diffusion equations in  exterior domains and in some domains with multiple cylindrical branches. In  exterior domains we show that all transition fronts propagate with the same  global mean speed, which turns out to be equal to the uniquely defined planar  speed. In domains with multiple cylindrical branches, we show that the solutions  emanating from some branches and propagating completely are transition fronts  propagating with the unique planar speed. We also give some geometrical and  scaling conditions on the domain, either exterior or with multiple cylindrical  branches, which guarantee that any transition front has a global mean speed.