On a phase transition model

On a phase transition model

An Allen–Cahn phase transition model with a periodic nonautonomous term is presented for which an infinite number of transition states is shown to exist. A constrained minimization argument and the analysis of a limit problem are employed to get states having a finite number of transitions. A priori...

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Veröffentlicht in:Calculus of variations and partial differential equations 2013-05, Vol.47 (1-2), p.1-23
Hauptverfasser: Byeon, Jaeyoung, Rabinowitz, Paul H.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Approximation
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Decay
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Minimization
Optimization
Partial differential equations
Phase transformations
Phase transitions
Systems Theory
Theoretical
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Beschreibung
Zusammenfassung:An Allen–Cahn phase transition model with a periodic nonautonomous term is presented for which an infinite number of transition states is shown to exist. A constrained minimization argument and the analysis of a limit problem are employed to get states having a finite number of transitions. A priori bounds and an approximation procedure give the general case. Decay properties are also studied and a sharp transition result with an arbitrary interface is proved.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-012-0507-2