Existence and nonexistence of global solutions in time for a reaction-diffusion system with inhomogeneous terms

We consider the initial value problem for the reaction-diffusion system with inhomogeneous terms. In this paper we show the existence and nonexistence of global solution in time. Especially, for the nonexistence we extend the conditions of the nonlinear terms and the initial data to the weaker conditions. We prove that for the nonlinear term and the initial data whose support is included in some unbounded domain (for instance, the corn), there do not exist the global solutions in time.