GLOBAL EXISTENCE AND FINITE TIME QUENCHING FOR COUPLED SEMILINEAR PARABOLIC SYSTEMS

Abstract

In this paper, we study a parabolic system of two semilinear reaction diffusion equations with singular term in bounded domain ­Omega. It is proved that there exist a critical constant lambda* such that all nonnegative classical solutions are global if lambda1(­Omega) >lambda*, while if lambda1(­Omega) <lambda* all nonnegative classical solutions must quench in finite time, where lambda1(­Omega) is the first Dirichlet eigenvalue for the Laplacian operator on domain ­. Also, the upper and lower bound of quenching time is estimated.