Propagation dynamics of the Fisher-KPP nonlocal diffusion equation with free boundary

讲座时间 Datetime: 2022年6月18日，星期六， 14:30-16:00

地点 Venue: 腾讯线上会议：869967616 

 主持人 Host：唐德

报告人 Speaker:杜一宏

单位 Affiliation:澳大利亚新英格兰大学

报告摘要 Abstract:

Propagation has been modelled by reaction-diffusion equations since the pioneering works of Fisher and Kolmogorov-Peterovski-Piskunov (KPP). Much new developments have been achieved in the past several decades on the modelling of propagation, with traveling wave and related solutions playing a central role. In this talk, I will report some recent results obtained with several collaborators on the Fisher-KPP equation with free boundary and "nonlocal diffusion". A key feature of this nonlocal equation is that the propagation may or may not be determined by traveling wave solutions. There is a threshold condition on the kernel function which determines whether the propagation rate is linear or superlinear in time, also known as accelerated spreading in the latter case, where the rate of spreading is not determined by traveling waves. For some typical kernel functions, sharp estimates of the spreading rate will be presented.