Relaxation of the curve shortening flow via the parabolic Ginzburg -Landau equation

Relaxation of the curve shortening flow via the parabolic Ginzburg -Landau equation

In this paper we study how to find solutions to the parabolic Ginzburg–Landau equation that as 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 up the extinction time of the curve. We show that...

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Veröffentlicht in:Calculus of variations and partial differential equations 2008-03, Vol.31 (3), p.359-386
1. Verfasser: Trumper, Mariel Sáez
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematical problems
Mathematics
Mathematics and Statistics
Nonlinear equations
Parabolas
Partial differential equations
Systems Theory
Theoretical
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Zusammenfassung:In this paper we study how to find solutions to the parabolic Ginzburg–Landau equation that as 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 up the extinction time of the curve. We show that after the extinction time the solution converges uniformly to a constant.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-007-0118-5