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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

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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