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This paper deals with the blow-up of the solution to a non-local reaction diffusion problem in \(\mathbb{R}^{N}\) for \(N\geq3\) under nonlinear boundary conditions. Utilizing the technique of a differential inequality, lower bounds for the blow-up time are derived when the blow-up does occur under some suitable assumptions.

Lower bounds for the blow-up time of the nonlinear non-local reaction diffusion problems in R N ( N ≥ 3 )