Bounds for blow-up time for the heat equation under nonlinear boundary conditions
Lawrence Edward Payne, Philip W. Schaefer · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2009
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.