Blow-up results for evolution problems with inhomogeneous nonlocal diffusion

We provide a sufficient condition on the existence and nonexistence of global positive solutions to the Cauchy problem for an inhomogeneous nonlocal diffusion ut=J⁎u−u+up+f(x)ut=J⁎u−u+up+f(x), where J   is a nonnegative function, p>0p>0, and f≥0,≢0f≥0,≢0. Meanwhile, the case of an inhomogeneous nonlocal diffusion system is considered. It turns out that the inhomogeneous terms substantially contribute to the blow-up exponent, which coincides with the classical one when the diffusion is given by the Laplacian.