Global Existence And Finite Time Blow-up For A Nonlinear Reaction Diffusion System

In this paper, we consider the global existence and blow-up in finite tifne of the solutions for the non-linear parabolic system:with homogeneous Dirichlet boundary data. We take the method of upper and lower solutions to investigate some conditions under which the solutions of the above nonlinear reaction diffusion system existence global, and use convex functional method to study the blow-up solution. We will prove that whenp1>1, or q2 > 1 , or (1 -p1)(1 - q2_ < p2q1 , both global existence andblow-up in finite time of nonnegative solution depend on the magnitude of the initial data and the domain. In addition, when p1 < 1 , q2 < 1 , the results about the solutions which exist global or blow up in finite time depend crucially on the sign of difference (1 - p1 )(1 - q2) - p2 q1, the magnitude of theinitial data and the domain.