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: { u t = ( | u x | p 1 − 1 u x ) x + ∫ 0 a v m 1 ( ξ , t ) d ξ , ( x , t ) in [ 0 , a ] × ( 0 , T ) , v t = ( | v x | p 2 − 1 v x ) x + ∫ 0 a u m 2 ( ξ , t ) d ξ , ( x , t ) in [ 0 , a ] × ( 0 , T ) , with nonlinear boundary conditions u x | x = 0 = 0 , u x | x = a = u q 11 v q 12 | x = a , v x | x = 0 = 0 , v x | x = a = u q 21 v q 22 | x = a and the initial data ( u 0 , v 0 ), where p 1 , p 2 > 1 , m 1 , m 2 , q 11 , q 12 , q 21 , q 22 > 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.