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Degenerate Diffusions pp 19–60Cite as

Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 47))

Abstract

The use of parabolic double obstacles problems for approximating curvature dependent phase boundary motion is reviewed. It is shown that such problems arise naturally in multi-component diffusion with capillarity. Formal matched asymptotic expansions are employed to show that phase field models with order parameter solving an obstacle problem approximate curvature dependent phase boundary motion. Numerical simulations of surfaces evolving according to their mean curvature are presented.

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Author information

Authors and Affiliations

  1. Mathematics Division, University of Sussex, Brighton, BN1 9QH, UK

    J. F. Blowey & C. M. Elliott

Authors
  1. J. F. Blowey
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  2. C. M. Elliott
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Wei-Ming Ni

  2. University of Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

    L. A. Peletier

  3. Division de Matemáticas, Universidad Autonomade Madrid, Cantoblanco, 28049, Madrid, Spain

    J. L. Vazquez

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© 1993 Springer-Verlag Berlin Heidelberg

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Blowey, J.F., Elliott, C.M. (1993). Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems. In: Ni, WM., Peletier, L.A., Vazquez, J.L. (eds) Degenerate Diffusions. The IMA Volumes in Mathematics and its Applications, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0885-3_2

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  • DOI: https://doi.org/10.1007/978-1-4612-0885-3_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6935-9

  • Online ISBN: 978-1-4612-0885-3

  • eBook Packages: Springer Book Archive

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