报告题目： The asymptotic propagation speed of the Fisher-KPP equation with effective boundary condition on a road

报 告 人：王学锋教授 香港中文大学（深圳）

报告时间：2021年5月20日 9:30-10:30

报告地点：腾讯会议 ID：567 637 490

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校内联系人：刘长春 liucc@jlu.edu.cn

报告摘要：

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.

报告人简介：

王学锋，香港中文大学（深圳）教授，博士生导师，研究生院副经理。于2019年8月加入香港中文大学（深圳）。在此之前，他在美国杜兰大学工作了26年，2016-2019年在南方科技大学任职。主要研究方向是偏微分方程及其应用。在CPAM、Duke Math. J、Arch. Ration. Mech. Anal.、SIAM J. Math. Anal.、Comm. Math. Phy.等高水平杂志上发表论文几十篇，现担任多个国际重要数学杂志的编委或副主编。