In this paper, we consider the following reaction diffusion equations under Dirichlet boundary conditionwhere Ω is a bounded domain of R N (N ≥ 2) with smooth boundary ∂Ω. By constructing some appropriate auxiliary functions and using a first-order differential inequality technique, the upper and lower bounds on blow-up time when blow-up occurs are presented. Moreover, conditions on the data to ensure that the solution exists globally or blows up at some finite time are also derived.

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