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The asymptotic propagation speed of the Fisher-KPP equation with effective boundary condition on a road
王学锋 教授(香港中文大学(深圳))
2021年3月5日14:00-15:00  腾讯会议ID:325 178 798

*主持人:何小清 青年研究员
*时间:2021年3月5日14:00-15:00
*地点:腾讯会议ID:325 178 798(https://meeting.tencent.com/s/ZMEisqkRm3oN)


*讲座内容简介:
Of concern is the Fisher-KPP equation on the xy-plane with an “effective boundary condition” imposed on the x-axis. This model, recently derived by Huicong Li and me, is meant to model the scenario of fast diffusion on a “road” in a large “field”. In our work, the asymptotic propagation speed of this model in the horizontal direction is obtained, showing that the fast diffusion on the road does enhance spreading speed in the horizontal direction in the field. In the new joint work with Xinfu Chen and Junfeng He, we study the propagation speed in ALL directions, showing that away from the $y-$axis by a certain angle (which can be explicitly calculated in terms of parameters), the fast diffusion on the x-axis increases propagation speed, with the speed getting larger when the direction is closer to the x-axis. We also obtain the asymptotic spreading shape for the model. These results are parallel to the ones obtained by Berestycki et al. for a different model which is meant to model the same physical phenomenon. However, our method differs from theirs in that we are forced to abandon the idea using lower solutions (when deriving a lower bound for the spreading speed) and have to use the fundamental solution of the linearized problem to come up with very delicate lower bound estimates for the nonlinear problem.

*主讲人简介:
王学锋教授于2019年8月加入香港中文大学(深圳)。在此之前,他在杜兰大学工作了26年,2016-2019年在南方科技大学任职。王学锋教授的研究领域是偏微分方程(PDE)。他的一些研究课题旨在通过典范的例子在简洁的框架下发现新的数学现象,提供新的视角,展示新的方法。其它的课题(例如大范围分支理论和Krein-Rutman理论)是为分析应用中出现的日益复杂的PDE模型提供通用的、易操作的工具。