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Saddle solutions of the bistable diffusion equation

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Abstract

Stationary solutions of the bistable Cahn-Allen diffusion equation in the plane are constructed, which are positive in quadrants 1 and 3 and negative in the other two quadrants. They are unique and obey certain monotonicity and limiting properties. Solutions of the dynamic problem near this stationary solution generally split the cross-shaped nullset into two disconnected parts which remain bounded away from each other.

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Authors and Affiliations

  1. University of Utah, Salt Lake City, USA

    Ha Dang & Paul C. Fife

  2. University of Leiden, The Netherlands

    L. A. Peletier

Authors
  1. Ha Dang
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  2. Paul C. Fife
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  3. L. A. Peletier
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Dedicated to Klaus Kirchgässner on the occasion of his 60th birthday

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Dang, H., Fife, P.C. & Peletier, L.A. Saddle solutions of the bistable diffusion equation. Z. angew. Math. Phys. 43, 984–998 (1992). https://doi.org/10.1007/BF00916424

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  • DOI: https://doi.org/10.1007/BF00916424

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