Global existence and blow-up of solutions to an evolution p-Laplace system coupled via nonlocal sources

The aim of this paper is to investigate the behavior of positive solutions to the following system of evolution p-Laplace equations coupled via nonlocal sources:{ut=(|ux|p1−1ux)x+∫0avm1(ξ,t)dξ,(x,t) in [0,a]×(0,T),vt=(|vx|p2−1vx)x+∫0aum2(ξ,t)dξ,(x,t) in [0,a]×(0,T), with nonlinear boundary conditions ux|x=0=0ux|x=0=0, ux|x=a=uq11vq12|x=aux|x=a=uq11vq12|x=a, vx|x=0=0,vx|x=a=uq21vq22|x=avx|x=0=0,vx|x=a=uq21vq22|x=a and the initial data (u0u0, v0v0), where p1,p2>1p1,p2>1, m1,m2,q11,q12,q21,q22>0m1,m2,q11,q12,q21,q22>0. Under appropriate hypotheses, the authors first prove a local existence result by a regularization method. Then the authors discuss the global existence and blow-up of positive weak solutions by using a comparison principle.