Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Convergence rate in the weighted norm for a semilinear heat equation with supercritical nonlinearity
Yūki Naito
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2014 Volume 37 Issue 3 Pages 646-667

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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.
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© 2014 Department of Mathematics, Tokyo Institute of Technology
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