报告题目：Effects of some new free boundary conditions on the nonlocal KPP equation with free boundary

报告时间：2024-10-25   10:30-11:30

报  告 人 ：杜一宏  院士 （澳大利亚新英格兰大学）

报告地点：理学院东北楼四楼报告厅（404）

Abstract：I will report some recent results on the nonlocal reaction diffusion equation u_t-dL[u]=f(u) with a KPP type reaction term 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 nonlocal diffusion operator L[u] has the form

L[u](t,x)=∫2_g(t)^h(t)▒J (x-y)u(t,y)dy-u(t,x)

while the free boundaries are governed by

h’(t)=μ∫2_g(t)^h(t)▒K (h(t)-x)u(t,x)dx,

g’(t)=-μ∫2_g(t)^h(t)▒K (x-g(t))u(t,x)dx,

as well as u(t,g(t))=u(t,h(t))=0, where K(z) is nonnegative and continuous for z≥0 with K(0)>0.

Depending on the relationships between K and J, new behavior may appear. The basic model of Cao-Du-Li-Li (JFA2019) corresponds to the case that K(z)=∫2_z^∞▒J (x)dx. Some new relations between J and K will be examined.

The talk is based on joint works with Xin Long, Wenjie Ni, Fernando Quiros and Taishan Yi.