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Geometric Conditions on Free Boundaries

In: Geometric Analysis and Nonlinear Partial Differential Equations

Author

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  • Reiner Schätzte

    (der Rheinischen Friedrich-Wilhelms-Universität Bonn, Mathematisches Institut)

Abstract

Summary On free boundaries arising in models for melting and solidification of materials, conditions are often prescribed using geometrical data of the free boundary. In smooth models approximating these free boundary problems, the geometric conditions are replaced by elliptic and parabolic equations. We describe the approximation of mean curvature flow by the Allen- Cahn equation, also with coupling, and of the Stefan problem with Gibbs-Thomson law by the quasi-stationary phase field equations.

Suggested Citation

  • Reiner Schätzte, 2003. "Geometric Conditions on Free Boundaries," Springer Books, in: Stefan Hildebrandt & Hermann Karcher (ed.), Geometric Analysis and Nonlinear Partial Differential Equations, pages 201-216, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55627-2_13
    DOI: 10.1007/978-3-642-55627-2_13
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