| Abstract: | In this paper, we study the following semilinear integro‐differential equation of the parabolic type that arise in the theory of nuclear reactor kinetics:  under homogeneous Dirichlet boundary condition, where p, q⩾1. We first establish the local solvability of a large class of semilinear non‐local equations including the above equation. Next, we give the finite time blow‐up result by some modification of Kaplan's method and also the existence of global solutions by the comparison method. Copyright © 1999 John Wiley & Sons, Ltd. |
