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Global Existence and Stability of Solutions to the Phase Field Equations

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Free Boundary Value Problems

Abstract

The global existence of smooth solutions to the initial boundary value problems of the phase field equations is proved which improves the corresponding results by Caginalp. The asymptotic behaviour of solutions as t → +∞ and the corresponding stationary problems are also extensively studied.

On leave from Institute of Mathematics, Fudan University, Shanghai, China. This work is partially supported by SFB 256 at Bonn University and the National Science Foundation of China.

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References

  1. G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rat. Mech. Anal., 92 (1986), 205–245

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Author information

Authors and Affiliations

  1. Mathematics Division, University of Sussex, Falmer Brighton, BN1 9QH, Great Britain

    C. M. Elliott

  2. Institute of Mathematics, Fudan University, Shanghai, People’s Republic Of China

    Zheng Songmu

Authors
  1. C. M. Elliott
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  2. Zheng Songmu
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Universitätsstrasse 8, D-8900, Augsburg, Germany

    K.-H. Hoffmann

  2. Fachbereich 10 — Bauwesen, Universität-GH Essen, Postfach 103 764, D-4300, Essen, Germany

    J. Sprekels

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© 1990 Birkhäuser Verlag Basel

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Elliott, C.M., Songmu, Z. (1990). Global Existence and Stability of Solutions to the Phase Field Equations. In: Hoffmann, KH., Sprekels, J. (eds) Free Boundary Value Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 95. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7301-7_4

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  • DOI: https://doi.org/10.1007/978-3-0348-7301-7_4

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-7643-2474-2

  • Online ISBN: 978-3-0348-7301-7

  • eBook Packages: Springer Book Archive

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