Multi-clustered high-energy solutions for a phase transition problem
Published online by Cambridge University Press: 12 July 2007
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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