Bounds for blow-up time for the heat equation under nonlinear boundary conditions

L. E. Payne; P. W. Schaefer

doi:10.1017/S0308210508000802

Abstract

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A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a sufficient condition which implies that blow-up does occur is determined.

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Bounds for blow-up time for the heat equation under nonlinear boundary conditions

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