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

Saez Trumper, Mariel

doi:10.1007/s00526-007-0118-5

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

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Saez Trumper, Mariel
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-63A5-5

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.