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Relaxation of the Curve Shortening Flow via the Parabolic Ginzburg-Landau equation

Saez Trumper, M. (2008). Relaxation of the Curve Shortening Flow via the Parabolic Ginzburg-Landau equation. Calculus of Variations and Partial Differential Equations, 31(3), 359-386. doi:10.1007/s00526-007-0118-5.

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Calc31-359.pdf (Publisher version), 367KB
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Creators:
Saez Trumper, Mariel1, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24012

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Abstract: In this paper we study how to find solutions $$u_\epsilon$$ to the parabolic Ginzburg–Landau equation that as $$\epsilon \to 0$$ have as interface a given curve that evolves under curve shortening flow. Moreover, for compact embedded curves we find a uniform profile for the solution $$u_\epsilon$$ up the extinction time of the curve. We show that after the extinction time the solution converges uniformly to a constant.

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Dates: 2008-03
Publication Status: Published in print
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Identifiers: DOI: 10.1007/s00526-007-0118-5
eDoc: 316933
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Title: Calculus of Variations and Partial Differential Equations
Source Genre: Journal
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Pages: - Volume / Issue: 31 (3) Sequence Number: - Start / End Page: 359 - 386 Identifier: ISSN: 1432-0835