Abstract
This paper deals with the blow-up of the solution to a non-local reaction diffusion problem in R N for N≥3 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.MSC: 35K20, 35K55, 35K65.
Highlights
1 Introduction There is a vast literature on the question of blow-up of solutions to nonlinear parabolic equations and systems
We consider the blow-up for the solution of the following nonlinear non-local reaction diffusion problems, which have been studied by Song in [ ]:
In [, – ], the authors have studied the question of blow-up for the solution of parabolic problems by imposing two different nonlinear boundary conditions: homogeneous Dirichlet boundary conditions or homogeneous Neumann boundary conditions
Summary
1 Introduction There is a vast literature on the question of blow-up of solutions to nonlinear parabolic equations and systems. One would like to know among other things whether the solution blows up. We consider the blow-up for the solution of the following nonlinear non-local reaction diffusion problems, which have been studied by Song in [ ]: Where is the Laplace operator, ∂ the boundary of and t∗ the possible blow-up time, p, q > .
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