Traveling fronts of curve flow with external force field

Abstract

This paper aims to classify all the traveling fronts of a curvature flow with external force fields in thetwo-dimensional Euclidean space, i.e., the curve is evolved by thesum 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 thetraveling fronts are of completely different geometry fornon-constant external force fields.