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This paper deals with the global existence and blow-up of the solution for a class of nonlinear reaction diffusion problems. The purpose of this paper is to establish conditions on the data to guarantee the blow-up of the solution at some finite time, and conditions to ensure that the solution remains global. In addition, an upper bound for the 'blow-up time', an upper estimate of the 'blow-up rate', and an upper estimate of the global solution are also specified. Finally, as applications of the obtained results, some examples are presented. [ABSTRACT FROM AUTHOR]