Radial terrace solutions and propagation profile of multistable reaction-diffusion equations over ${\mathbb{R}}^N$

Yihong Du, Hiroshi Matano

We study the propagation profile of the solution $u(x,t)$ to the nonlinear diffusion problem $u_t-\Delta u=f(u)(x\in {\mathbb{R}}^N,t>0)$, $u(x,0)=u_0(x)(x\in {\mathbb{R}}^N)$, where $…