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

Patricio L. Felmer, Salomé Martínez, Kazunaga Tanaka

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)731-765
Number of pages35
JournalRoyal Society of Edinburgh - Proceedings A
Volume135
Issue number4
DOIs
Publication statusPublished - 2005 Jan 1

ASJC Scopus subject areas

  • Mathematics(all)

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