Blow Up and Global Existence of Solutions to an Inhomogeneous Parabolic System

We study the critical phenomenon of a weakly coupled inhomogeneous parabolic system, which is largely unexplored even though the homogeneous problem has been widely studied. The conditions on the powers of the nonlinear terms are new compared with the well-known homogeneous case. The method appears to be different from the standard ones in the literature. An application to the Lamé– Emden system is also given