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

U2 - 10.1017/s0308210505000375

DO - 10.1017/s0308210505000375

M3 - Article

AN - SCOPUS:27644510749

SN - 0308-2105

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

IS - 4

ER -