Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I |
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Authors: | L E Payne G A Philippin and S Vernier Piro |
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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. |
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