Precise bounds for finite time blowup of solutions to very general one-space-dimensional nonlinear Neumann problems

Authors:
Kurt Bryan and Michael S. Vogelius

Journal:
Quart. Appl. Math. **69** (2011), 57-78

MSC (2000):
Primary 35B05, 35B40, 45D05, 45G10, 45M05

Published electronically:
January 20, 2011

MathSciNet review:
2807977

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we analyze the asymptotic finite time blowup of solutions to the heat equation with a nonlinear Neumann boundary flux in one space dimension. We perform a detailed examination of the nature of the blowup, which can occur only at the boundary, and we provide tight upper and lower bounds for the blowup rate for ``arbitrary'' nonlinear functions , subject to very mild restrictions.

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Additional Information

**Kurt Bryan**

Affiliation:
Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803

**Michael S. Vogelius**

Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

DOI:
http://dx.doi.org/10.1090/S0033-569X-2011-01203-2

Keywords:
Blowup,
heat equation,
nonlinear Neumann boundary condition

Received by editor(s):
June 2, 2009

Published electronically:
January 20, 2011

Article copyright:
© Copyright 2011
Brown University