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Γ-limit for the extended Fisher–Kolmogorov equation

Published online by Cambridge University Press:  12 July 2007

D. Hilhorst ,
L. A. Peletier  and
R. Schätzle
D. Hilhorst
Affiliation:
Analyse Numérique et EDP, CNRS, et Université de Paris-Sud, 91405 Orsay, France
L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, The Netherlands
R. Schätzle
Affiliation:
Departement der Mathematik, ETH Zentrum, Zürich, Switzerland
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Abstract

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We consider the Lyapunov functional, of the rescaled Extended Fisher-Kolmogorov equation This is a fourth order generalization of the Fisher–Kolmogorov or Allen–Cahn equation. We prove that if ε → 0, then tends to the area functional in the sense of Γ-limits, where the transition energy is given by the one-dimensional kink of the Extended Fisher–Kolmogorov equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 1 , February 2002 , pp. 141 - 162
Copyright
Copyright © Royal Society of Edinburgh 2002