Blow-up and global existence to a degenerate reaction–diffusion equation with nonlinear memory

In this paper, we consider a degenerate reaction–diffusion equation uk t − u = uq t 0 up(x, s) ds, x ∈ Ω, t >0, with homogeneous Dirichlet boundary conditions, where p, q are nonnegative constants and 0 < k <1. The blow-up criteria and the blow-up rate are obtained. © 2006 Elsevier Inc. All rights reserved