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Bounds for blow-up time for the heat equation under nonlinear boundary conditions. (English) Zbl 1184.35077

Summary: 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.

MSC:

35B44 Blow-up in context of PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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