学　术

教师发展中心“学者论坛”活动特别邀请澳大利亚科学院院士、新英格兰大学Du Yihong教授来校作学术交流。具体安排如下，欢迎广大师生参加。

一、主　题：Propagation dynamics of reaction-diffusion equations with a new free boundary condition

二、时　间：2024年5月3日10:00-11:30

三、地　点：清水河校区6号科研楼A648

四、主讲人：澳大利亚科学院院士、新英格兰大学 Du Yihong 教授

五、主持人：数学科学学院 向昭银 教授

六、内容简介：

 I will report some recent results on the reaction diffusion equation u_t-du_{xx}=f(u) with standard nonlinear functions f(u) over a changing interval [g(t), h(t)], viewed as a model for the spreading of a species with population range [g(t), h(t)] and density u(t,x).The free boundaries x=g(t) and x=h(t) are not governed by the same Stefan condition as in Du and Lin (2010) and other previous works; instead, they satisfy a related but different set of equations obtained from a “preferred population density” assumption at the range boundary, which allows the population range to shrink as well as to expand. I will demonstrate that the longtime dynamics of the model exhibits persistent propagation with a finite asymptotic propagation speed determined by a certain semi-wave solution, and the density function converges to the semi-wave profile as time goes to infinity. The asymptotic propagation speed is always smaller than that of the corresponding classical Cauchy problem where the reaction-diffusion equation is satisfied for x over the entire real line with no free boundary. Moreover, when the preferred population density used in the free boundary condition converges to 0, the solution $u$ of our free boundary problem converges to the solution of the corresponding classical Cauchy problem, and the propagation speed also converges to that of the Cauchy problem.

七、主讲人简介：

Du Yihong，澳大利亚新英格兰大学教授， 澳大利亚科学院院士；1978至1988年在山东大学获得学士、硕士和博士学位；1988至1991年赴英国 Heriot-Watt University 大学做Research Fellow，1991至1992年在澳大利亚新英格兰大学做Research Fellow；历任新英格兰大学讲师、高级讲师、副教授、教授；2021年当选澳大利亚科学院院士；非线性泛函分析、偏微分方程及其应用领域的国际知名专家，使用非线性自由边界问题对扩散现象进行建模的先驱和领导者，解决了尖锐阈值、边界爆破、分岔和多重线性等公开问题；已在JEMS、ARMA、PLMS、JFA、JMPA、AIHP、IUMJ、CVPDE、JDE等国际一流数学期刊上发表学术论文170余篇，完全他引次数超过5000次，多次入选 Web of Science高被引学者。

八、主办单位：教师发展中心

　　承办单位：数学科学学院 生命科学学院