### 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 u_{ε}(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 language | English |
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Pages (from-to) | 731-765 |

Number of pages | 35 |

Journal | Royal Society of Edinburgh - Proceedings A |

Volume | 135 |

Issue number | 4 |

Publication status | Published - 2005 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Royal Society of Edinburgh - Proceedings A*,

*135*(4), 731-765.

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

Research output: Contribution to journal › Article

*Royal Society of Edinburgh - Proceedings A*, vol. 135, no. 4, pp. 731-765.

}

TY - JOUR

T1 - Multi-clustered high-energy solutions for a phase transition problem

AU - Felmer, Patricio L.

AU - Martínez, Salomé

AU - Tanaka, Kazunaga

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=27644510749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644510749&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:27644510749

VL - 135

SP - 731

EP - 765

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 4

ER -