Traveling fronts of curve flow with external force field

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July 2010, 9(4): 975-986. doi: 10.3934/cpaa.2010.9.975

Traveling fronts of curve flow with external force field

Huaiyu Jian ^1, , Hongjie Ju ^1, and Wei Sun ^2,

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

Received September 2009 Revised January 2010 Published April 2010

Abstract
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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.

Keywords: nonlinear ODE, traveling front, Curve flow, phase analysis..

Mathematics Subject Classification: Primary: 35J60, 35K45; Secondary: 52K44, 53A0.

Citation: Huaiyu Jian, Hongjie Ju, Wei Sun. Traveling fronts of curve flow with external force field. Communications on Pure & Applied Analysis, 2010, 9 (4) : 975-986. doi: 10.3934/cpaa.2010.9.975

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