Advances in Differential Equations

Convergence of solutions of a semilinear parabolic equation to selfsimilar solutions of the linear heat equation

Marek Fila, Michael Winkler, and Eiji Yanagida

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Abstract

We find the rate of convergence of solutions of a semilinear parabolic equation to selfsimilar solutions of the linear heat equation. In particular, we show that the rate is not affected by the nonlinearity for some range of parameters, while in a complementary range the rate depends explicitly on the nonlinearity.

Article information

Source
Adv. Differential Equations Volume 13, Number 11-12 (2008), 1131-1149.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867289

Mathematical Reviews number (MathSciNet)
MR2483133

Zentralblatt MATH identifier
1178.35068

Subjects
Primary: 35K58: Semilinear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35C06: Self-similar solutions 35K05: Heat equation 35K15: Initial value problems for second-order parabolic equations

Citation

Fila, Marek; Winkler, Michael; Yanagida, Eiji. Convergence of solutions of a semilinear parabolic equation to selfsimilar solutions of the linear heat equation. Adv. Differential Equations 13 (2008), no. 11-12, 1131--1149. https://projecteuclid.org/euclid.ade/1355867289.


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