The Riemann Problem of a System for a Phase Transition Problem

1999 ◽  
pp. 455-464 ◽  
Author(s):  
Harumi Hattori
Keyword(s):  
Phase Transition ◽  
Riemann Problem ◽  
Transition Problem ◽  
Phase Transition Problem

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

2005 ◽  
Vol 135 (4) ◽  
pp. 731-765
Author(s):  
Patricio L. Felmer ◽  
Salomé Martínez ◽  
Kazunaga Tanaka
Keyword(s):  
Phase Transition ◽  
Singular Perturbation ◽  
Energy Function ◽  
High Energy ◽  
Number Of Layers ◽  
Transition Problem ◽  
Phase Transition Problem ◽  
Positive Length ◽  
Limit Energy

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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