Blow-up for a degenerate reaction–diffusion system with nonlinear nonlocal sources

This paper investigates the global existence and blow-up of nonnegative solution of the system u t = Δ u m + u p 1 ∫ Ω v q 1 d x , v t = Δ v n + v p 2 ∫ Ω u q 2 d x , ( x , t ) ∈ Ω × ( 0 , T ) with homogeneous Dirichlet boundary conditions, where Ω ⊂ R N is a bounded domain with smooth boundary ∂ Ω , m, n > 1 , p 1 , p 2 , q 1 , q 2 > 0 . The results depend crucially on the number p i , q i , m, n, the domain Ω and the initial data u 0 ( x ) , v 0 ( x ) . Moreover, we obtain the blow-up rate of the blow-up solution under some appropriate hypotheses.