Differential and Integral Equations

Global attractivity and convergence rate in the weighted norm for a supercritical semilinear heat equation

Yūki Naito

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Abstract

We consider the behavior of solutions to the Cauchy problem for a semilinear heat equation with supercritical nonlinearity. We study the convergence of solutions to steady states in a weighted norm, and show the global attractivity property of steady states. We also give its convergence rate for a class of initial data. Proofs are given by a comparison method based on matched asymptotic expansion.

Article information

Source
Differential Integral Equations, Volume 28, Number 7/8 (2015), 777-800.

Dates
First available in Project Euclid: 11 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1431347863

Mathematical Reviews number (MathSciNet)
MR3345333

Zentralblatt MATH identifier
1363.35215

Subjects
Primary: 35K15: Initial value problems for second-order parabolic equations 35B35: Stability 35B40: Asymptotic behavior of solutions

Citation

Naito, Yūki. Global attractivity and convergence rate in the weighted norm for a supercritical semilinear heat equation. Differential Integral Equations 28 (2015), no. 7/8, 777--800. https://projecteuclid.org/euclid.die/1431347863


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