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Multi-clustered high-energy solutions for a phase transition problem

Published online by Cambridge University Press:  12 July 2007

Patricio L. Felmer ,
Salomé Martínez  and
Kazunaga Tanaka
Patricio L. Felmer
Affiliation:
Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile ([email protected])
Salomé Martínez
Affiliation:
Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile ([email protected])
Kazunaga Tanaka
Affiliation:
Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan([email protected])
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Abstract

We study the balanced Allen–Cahn problem in a singular perturbation setting. We are interested in the behaviour of clusters of layers, i.e. a family of solutions uε(x) with an increasing number of layers as ε → 0. In particular, we give a characterization of cluster of layers with asymptotically positive length by means of a limit energy function and, conversely, for a given admissible pattern, i.e. for a given a limit energy function, we construct a family of solutions with the corresponding behaviour.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 4 , August 2005 , pp. 731 - 765
Copyright
Copyright © Royal Society of Edinburgh 2005

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