Abstract
In this paper, we study the existence and nonexistence of the global solutions to nonlinear reaction‐diffusion equations where is the half‐space , is a nonnegative continuous function, and is a locally Lipschitz function with some additional properties. The purpose of this paper is to give a necessary and sufficient condition for the existence of global solutions as follows: There is no global solution for any nonnegative and nontrivial initial data if and only if for every . In fact, we introduce a very special curve in to obtain the lower bound of decay of the heat semigroup, which is essential to prove the main result.
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