Global existence and nonexistence for degenerate parabolic equations with nonlinear boundary flux

In this paper, by constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions of global existence for nonnegative solutions to a degenerate parabolic system with completely coupled boundary conditions, which generalize the recent results of, for instance, Cui [Z. Cui, Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions, Nonlinear Anal. 68 (2008) 3201-3208], Zhou-Mu [J.Zhou, C. Mu, Algebraic criteria for global existence or blow-up for a boundary coupled system of nonlinear diffusion equations, Appl. Anal. 86 (2007) 1185-1197] etc. (C) 2011 Elsevier Ltd. All rights reserved.