Uniform blow-up profiles for nonlinear and nonlocal reaction–diffusion equations

In this paper, we investigate the blow-up properties of positive solutions to the following integro-parabolic equations ut=Δu+eαu+γ−1|Ω|∫Ωeβudx, where α,β>0α,β>0 and γ>1γ>1, and Ω={x∈Rn:|x|