几何分析讨论班——Effects of some new free boundary conditions on the nonlocal KPP equation with free boundary

报告人：杜一宏（澳大利亚科学院院士，澳大利亚新英格兰大学教授）

时间：2024年9月18日，下午4:00-5:00

地点：海纳苑2幢206室

摘要：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

  $L[u](t,x)=\int_{g(t)}^{h(t)}J(x-y)u(t, y)dy-u(t,x)$

while the free boundaries are governed by

     $ h’(t)=\mu\int_{g(t)}^{h(t)}K(h(t)-x)u(t,x)dx$,

     $ g’(t)=-\mu\int_{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 $z\geq 0$ 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 $K(z)=\int_z^\infty J(x)dx$. 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 Tanshan Yi.

联系人：李奇睿（qi-rui.li@zju.edu.cn）