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On Thermodynamically Consistent Stefan Problems with Variable Surface Energy

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Abstract

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities, it is proved that it exists globally in time and converges towards an equilibrium of the problem. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable if surface heat capacity is small; however, if kinetic undercooling is absent, they are stable if surface heat capacity is sufficiently large.

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Authors and Affiliations

  1. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 60120, Halle, Germany

    Jan Prüss & Mathias Wilke

  2. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Gieri Simonett

Authors
  1. Jan Prüss
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  2. Gieri Simonett
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  3. Mathias Wilke
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Correspondence to Gieri Simonett.

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Communicated by P. Rabinowitz

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Prüss, J., Simonett, G. & Wilke, M. On Thermodynamically Consistent Stefan Problems with Variable Surface Energy. Arch Rational Mech Anal 220, 603–638 (2016). https://doi.org/10.1007/s00205-015-0938-y

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  • DOI: https://doi.org/10.1007/s00205-015-0938-y

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