Blow-up And Global Existence For A Degenerate Parabolic System

In this thesis, we consider positive solutions of a degenerate parabolic system with homogeneous Dirichlet boundary condition. It is proved that all positive solutions exist globally iff 12≥abλ, whereλ1 is the first eigenvalue of ? ? on ? with homogeneous Dirichlet boundary condition. At the same time, we also give a sufficient condition that a solution blows up in finite time and an upper estimate of maximal existence time.