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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Payne, L.E., Philippin, G.A. & Vernier Piro, S. Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I. Z. Angew. Math. Phys. 61, 999–1007 (2010). https://doi.org/10.1007/s00033-010-0071-6
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DOI: https://doi.org/10.1007/s00033-010-0071-6