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

Kurt Bryan; Michael S. Vogelius

doi:10.1090/S0033-569X-2011-01203-2

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

Kurt Bryan, Michael S. Vogelius

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 "rbitrary" nonlinear functions F, subject to very mild restrictions.

Original language	English (US)
Pages (from-to)	57-78
Number of pages	22
Journal	Quarterly of Applied Mathematics
Volume	69
Issue number	1
DOIs	https://doi.org/10.1090/S0033-569X-2011-01203-2
State	Published - 2011

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

Blowup
Heat equation
Nonlinear neumann boundary condition

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10.1090/S0033-569X-2011-01203-2

Cite this

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AB - 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 "rbitrary" nonlinear functions F, subject to very mild restrictions.

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KW - Nonlinear neumann boundary condition

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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