Differential and Integral Equations

Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition

Bei Hu

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Abstract

This paper establishes the blowup estimate near the blowup time for the heat equation $u_t = \Delta u$ with the nonlinear boundary condition $u_n = u^p$ on $\partial \Omega\times [0,T)$, where $\Omega$ is a bounded domain in $R^N$. It is proved that the blowup will not occur in the interior of the domain. The blowup rate is established under certain conditio

Article information

Source
Differential Integral Equations, Volume 9, Number 5 (1996), 891-901.

Dates
First available in Project Euclid: 6 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367871522

Mathematical Reviews number (MathSciNet)
MR1392086

Zentralblatt MATH identifier
0852.35072

Subjects
Primary: 35K60: Nonlinear initial value problems for linear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions

Citation

Hu, Bei. Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition. Differential Integral Equations 9 (1996), no. 5, 891--901. https://projecteuclid.org/euclid.die/1367871522


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