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

摘要

This paper investigates the global existence and blow-up of nonnegative solution of the systemut=Δum+up1∫Ωvq1dx,vt=Δvn+vp2∫Ωuq2dx,(x,t)∈Ω×(0,T)with homogeneous Dirichlet boundary conditions, where Ω⊂RN is a bounded domain with smooth boundary ∂Ω, m, n>1, p1, p2, q1, q2>0. The results depend crucially on the number pi, qi, m, n, the domain Ω and the initial data u0(x), v0(x). Moreover, we obtain the blow-up rate of the blow-up solution under some appropriate hypotheses.