Abstract
We consider the nonlinear heat equation with nonlocal reaction term in space u t−Δu= ∫ Ω u p , in smoothly bounded domains. We prove the existence of a universal bound for all nonnegative global solutions of this equation. Moreover, in contrast with similar recent results for equations with local reaction terms, this is shown to hold for all p>1. As an interesting by-product of our proof, we derive for this equation a smoothing effect under weaker assumptions than for corresponding problem with local reaction.
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