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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

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: 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 $ F$, 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
PII: S 0033-569X(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



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