Ginzburg-Landau equation and motion by mean curvature, II: Development of the initial interface |
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Authors: | Halil Mete Soner |
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Institution: | (1) Department of Mathematics, Carnegie Mellon University, 15213-3890 Pittsburgh, PA |
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Abstract: | In this paper, we study the short time behavior of the solutions of a sequence of Ginzburg-Landau equations indexed by ∈.
We prove that under appropriate assumptions on the initial data, solutions converge to ±1 in short time and behave like the
one-dimensional traveling wave across the interface. In particular, energy remains uniformly bounded in ∈.
Partially supported by the NSF Grant DMS-9200801 and by the Army Research Office through the Center for Nonlinear Analysis. |
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Keywords: | Math Subject Classification" target="_blank">Math Subject Classification 35A05 35K57 |
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