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，香港中文大学 （深圳）
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：王学锋教授，偏微分方程专家。1984年于北京大学数学系获学士学位，1990年于美国明尼苏达大学数学学院获博士学位。 1990年至2016年在美国Tulane大学数学系工作、任终身教授；2016年-2019年在南方科技大学工作，任讲席教授、数学系副主任和学校教师会会长；2019年至今在香港中文大学（深圳）任校长讲座教授、研究生院院长。主要研究领域是偏微分方程及其应用，研究方向涉及椭圆算子的特征值问题、整体分叉理论改进与应用、趋化模型解的渐近性分析、间断系数的抛物、椭圆边值问题的实效边值问题和渐近波速研究等；多篇论文为开创性研究工作和高被引论文，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。
报告时间：2022年6月2日 14:00-15:30
报告地点：腾讯会议ID：513 642 621
主办单位：伟德国际1946源自英国
