Kodai Mathematical Journal

Convergence rate in the weighted norm for a semilinear heat equation with supercritical nonlinearity

Yūki Naito

Full-text: Open access

Abstract

We study the behavior of solutions to the Cauchy problem for a semilinear heat equation with supercritical nonlinearity. It is known that two solutions approach each other if these initial data are close enough near the spatial infinity. In this paper, we give its sharp convergence rate in the weighted norms for a class of initial data. Proofs are given by a comparison method based on matched asymptotics expansion.

Article information

Source
Kodai Math. J., Volume 37, Number 3 (2014), 646-667.

Dates
First available in Project Euclid: 30 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1414674614

Digital Object Identifier
doi:10.2996/kmj/1414674614

Mathematical Reviews number (MathSciNet)
MR3273889

Zentralblatt MATH identifier
1323.35059

Citation

Naito, Yūki. Convergence rate in the weighted norm for a semilinear heat equation with supercritical nonlinearity. Kodai Math. J. 37 (2014), no. 3, 646--667. doi:10.2996/kmj/1414674614. https://projecteuclid.org/euclid.kmj/1414674614


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