Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms

This paper considers the blow‐up phenomena for the following reaction‐diffusion problem with nonlocal and gradient terms: Here m > 1, and Ω ⊂ ℝ N ( N ≥ 2) is a bounded and convex domain with smooth boundary. Applying a Sobolev inequality and a differential inequality technique, lower bounds for blow‐up time when blow‐up occurs are given. Moreover, two examples are given as applications to illustrate the abstract results obtained in this paper.

Abstract licence: CC BY

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