Traveling fronts of curve flow withexternal force field

Huaiyu Jian; Hongjie Ju; Wei Sun

doi:10.3934/cpaa.2010.9.975

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2010, Volume 9, Issue 4: 975-986. Doi: 10.3934/cpaa.2010.9.975

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Traveling fronts of curve flow with external force field

1.
Department of Mathematical Sciences, Tsinghua University, Beijing 100084
2.
Department of Mathematics, Ohio State University, Columbus, 43210

Received: August 31, 2009

Revised: December 31, 2009

Published: June 2010

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Abstract

This paper aims to classify all the traveling fronts of a curvature flow with external force fields in the two-dimensional Euclidean space, i.e., the curve is evolved by the sum of the curvature and an external force field. We show that any traveling front is either a line or Grim Reaper if the external force field is constant. However, we find that the traveling fronts are of completely different geometry for non-constant external force fields.

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Mathematics Subject Classification: Primary: 35J60, 35K45; Secondary: 52K44, 53A05.

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