学术报告

题      目：Reaction-diffusion fronts in funnel-shaped domains

报  告  人：张明敏  博士  (邀请人：丁维维 )

                                  法国图卢兹三大

时      间：9月4日  15：00-16：00

地     点：数科院东楼401

报告人简介:

        张明敏，现为法国图卢兹三大博士后，合作导师为Gregory Faye研究员和Jean-Michel Roquejoffre.教授。于2021年12月获得中国科学技术大学和法国艾克斯马赛大学博士学位，导师为梁兴教授和Francois Hamel教授。研究兴趣为反映扩散方程的动力学及传播现象、传染病模型等。目前已在AIHP、JMPA、Adv. Math. 等杂志上发表论文。

摘      要：

       We consider bistable reaction-diffusion equations in funnel-shaped domains of \mathbb{R}^N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front in the straight part of such a domain and moving into the conical part. We show a dichotomy between blocking and spreading, by proving especially some new Liouville type results on stable solutions of semilinear elliptic equations in the whole space \mathbb{R}^N. We also show that any spreading solution is a transition front having a global mean speed, which is the unique speed of planar fronts, and that it converges at large time in the conical part of the domain to a well-formed front whose position is approximated by expanding spheres. Moreover, we provide sufficient conditions on the size R of the straight part of the domain and on the opening angle \alpha of the conical part, under which the solution emanating from a planar front is blocked or spreads completely in the conical part. This is a joint work with Prof. François Hamel.