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Published in:
1992 | OriginalPaper | Chapter
Phase Field Equations in the Singular Limit of Sharp Interface Problems
Authors : Gunduz Caginalp, Xinfu Chen
Published in: On the Evolution of Phase Boundaries
Publisher: Springer New York
Included in: Professional Book Archive
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In one of the singular limits as interface thickness approaches zero, solutions to the phase field equations formally approach those of a sharp interface model which incorporates surface tension. Here, we use a modification of the original phase field equations and prove this convergence rigorously in the one-dimensional and radially symmetric cases. Convergence to motion by mean curvature in another distinguished limit is also proved.