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          Institute: MPI für Gravitationsphysik     Collection: Geometric Analysis and Gravitation     Display Documents



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ID: 316933.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
Relaxation of the Curve Shortening Flow via the Parabolic Ginzburg-Landau equation
Authors:Saez Trumper, Mariel
Date of Publication (YYYY-MM-DD):2008-03
Title of Journal:Calculus of Variations and Partial Differential Equations
Volume:31
Issue / Number:3
Start Page:359
End Page:386
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
Identifiers:ISSN:1432-0835
DOI:10.1007/s00526-007-0118-5
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