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Action minimization for an Allen-Cahn equation with an unequal double-well potential

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Abstract

We consider the minimization problem of the Allen-Cahn action functional with an unequal double-well potential. For the stochastic Allen-Cahn equation switching from one stable state to the other rarely occurs. The probability of switching is determined by the minimum of the action functional. We give an explicit description of the minimum and its optimal path in one-dimension.

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  1. Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Yuko Nagase

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  1. Yuko Nagase
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Correspondence to Yuko Nagase.

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Nagase, Y. Action minimization for an Allen-Cahn equation with an unequal double-well potential. manuscripta math. 137, 81–106 (2012). https://doi.org/10.1007/s00229-011-0458-5

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  • DOI: https://doi.org/10.1007/s00229-011-0458-5

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