A diffusive logistic equation with concentrated and nonlocal sources

In this paper, we study a reaction‐diffusion equation where nonlinear memory and concentration effects are considered at the same time. We are specially concerned with the local solvability of this problem for singular initial data in Lebesgue spaces. We also analyze the vanishing concentration problem and prove a blow‐up alternative. Copyright © 2017 John Wiley & Sons, Ltd.