A degenerate and singular parabolic system coupled through boundary conditions

The paper deals with the global existence and nonexistence for degenerate and singular parabolic system with nonlinear boundary condition. By using the comparison principle and constructing the self-similar super-solution and sub-solution, we obtain the critical global existence curve. The critical curve of Fujita type is conjectured with the aid of some new results. An interesting feature of our results is that the critical global existence curve and the critical Fujita curve are determined by a matrix and by the solution of a linear algebraic system, respectively.