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

Patricio L. Felmer, Salomé Martínez, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    8 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
    Publication statusPublished - 2005

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    High Energy
    Phase Transition
    Phase transitions
    Energy Function
    Singular Perturbation
    Family

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Multi-clustered high-energy solutions for a phase transition problem. / Felmer, Patricio L.; Martínez, Salomé; Tanaka, Kazunaga.

    In: Royal Society of Edinburgh - Proceedings A, Vol. 135, No. 4, 2005, p. 731-765.

    Research output: Contribution to journalArticle

    Felmer, Patricio L. ; Martínez, Salomé ; Tanaka, Kazunaga. / Multi-clustered high-energy solutions for a phase transition problem. In: Royal Society of Edinburgh - Proceedings A. 2005 ; Vol. 135, No. 4. pp. 731-765.
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