“…The main concerns in the above works are for the existence of a global solution and the blow-up property of the solution. In particular, the works in [20,21] deal with the Cauchy problem in the one-spatial dimensional case with D(u) = u σ and f (u) = u β , for some positive constants σ and β; those in [5,24,40,41,46] treat the Cauchy problem with more general equations; those in [6,13,42,44] consider initial-boundary value problems in a bounded domain with either the Neumann type or the mixed type boundary conditions; and that in [31] deals with the Dirichlet boundary condition. The global existence and blow-up problem has been extended in [11,12,16,17,22,23,28,45] Recently the authors treated a general coupled system of N equations in the form of (1.1) but with non-linear boundary conditions (cf.…”