On the set of solutions to a variational phase transition problem of continuum mechanics

2007 ◽  
Vol 144 (6) ◽  
pp. 4645-4654 ◽  
Author(s):  
V. G. Osmolovskii
Author(s):  
Patricio L. Felmer ◽  
Salomé Martínez ◽  
Kazunaga Tanaka

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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