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Solutions for the Two-Phase Stefan Problem with the Gibbs—Thomson Law for the Melting Temperature

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Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids

Abstract

The coupling of the Stefan equation for the heat flow with the Gibbs-Thomson law relating the melting temperature to the mean curvature of the phase interface is considered. Solutions, global in time, are constructed which satisfy the natural a priori estimates. Mathematically the main difficulty is to prove a certain regularity in time for the temperature and the indicator function of the phase separately. A capacity type estimate is used to give an Lx bound for fractional time derivatives.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 6, 5300, Bonn, West Germany

    Stephan Luckhaus

Authors
  1. Stephan Luckhaus
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Editor information

Editors and Affiliations

  1. Mathematical Institute, 24-29 St. Giles, Oxford, OX1 3LB, UK

    John M. Ball

  2. Department of Mathematics, Carnegie-Mellon University, PA 15213-3890, Pittsburgh, USA

    David Kinderlehrer

  3. Dipartimento di Ingegneria Civile, Universitá di Roma “Tor Vergata”, I-00133, Roma, Italy

    Paulo Podio-Guidugli

  4. Center for Mathematical Sciences, University of Wisconsin, 1308 West Dayton St., WI 53715-1149, Madison, USA

    Marshall Slemrod

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© 1999 Springer-Verlag Berlin Heidelberg

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Luckhaus, S. (1999). Solutions for the Two-Phase Stefan Problem with the Gibbs—Thomson Law for the Melting Temperature. In: Ball, J.M., Kinderlehrer, D., Podio-Guidugli, P., Slemrod, M. (eds) Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59938-5_12

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  • DOI: https://doi.org/10.1007/978-3-642-59938-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64188-6

  • Online ISBN: 978-3-642-59938-5

  • eBook Packages: Springer Book Archive

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