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Traveling fronts of curve flow with external force field

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


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