報告題目： The asymptotic propagation speed of the Fisher-KPP equation with effective boundary condition on a road
報 告 人：王學鋒教授 香港中文大學（深圳）
報告時間：2021年5月20日 9:30-10:30
報告地點：騰訊會議 ID：567 637 490
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校内聯系人：劉長春 liucc@jlu.edu.cn
報告摘要：
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.
報告人簡介：
王學鋒，香港中文大學（深圳）教授，博士生導師，研究生院副院長。于2019年8月加入香港中文大學（深圳）。在此之前，他在美國杜蘭大學工作了26年，2016-2019年在南方科技大學任職。主要研究方向是偏微分方程及其應用。在CPAM、Duke Math. J、Arch. Ration. Mech. Anal.、SIAM J. Math. Anal.、Comm. Math. Phy.等高水平雜志上發表論文幾十篇，現擔任多個國際重要數學雜志的編委或副主編。
