Global existence and blow-up for degenerate and singular parabolic system with localized sources

This paper deals with the blow-up properties of the solution to degenerate and singular parabolic system with localized sources and homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally and blows up in finite time are obtained. Furthermore, under certain conditions, it is proved that the blow-up set of the solution is the whole domain.