BLOW-UP PHENOMENA FOR A SEMILINEAR HEAT EQUATION WITH NONLINEAR BOUNDARY CONDITION, I

L. E. PAYNE;G. A. PHILIPPIN;PIRO, STELLA

2010-01-01

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Abstract

We consider the blow-up of the solution to a semilinear heat equation with nonlinear boundary condition. We establish conditions on nonlinearities sufficient to guarantee that u(x, t) exists for all time t > 0 as well as conditions on data forcing the solution u(x, t) to blow up at some finite time t∗. Moreover, an upper bound for t∗ is derived. Under somewhat more restrictive conditions, lower bounds for t* are also derived.