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On a phase transition model

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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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Authors and Affiliations

  1. Department of Mathematics, POSTECH, San 31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk, 790-784, Republic of Korea

    Jaeyoung Byeon & Paul H. Rabinowitz

  2. Department of Mathematics, University of Wisconsin Madison, Madison, WI, 53706, USA

    Paul H. Rabinowitz

Authors
  1. Jaeyoung Byeon
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  2. Paul H. Rabinowitz
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Correspondence to Paul H. Rabinowitz.

Additional information

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

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