Asymptotic behavior of the nonlocal diffusion equation with localized source
Asymptotic behavior of the nonlocal diffusion equation with localized source
In this paper we study the nonlocal diffusion equation with localized source: $u_t= J*u-u+a(x)u^p$ in $\mathbb {R}^N\times (0,T)$, with $a(x)$ nonnegative, continuous, and compactly supported. It is found that the localized source $a(x)$ drastically changes the asymptotic behavior of the nonlocal diffusion equation that the Fujita phenomenon happens only if …