Abstract
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.
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Communicated by A. Malchiodi.
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Byeon, J., Rabinowitz, P.H. On a phase transition model. Calc. Var. 47, 1–23 (2013). https://doi.org/10.1007/s00526-012-0507-2
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DOI: https://doi.org/10.1007/s00526-012-0507-2