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.
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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 -