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

Abstract In this paper, we consider a degenerate reaction–diffusion equation ( u k ) t − Δ u = u q ∫ 0 t u p ( x , s ) d s , 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.