Mean curvature flow with driving force on fixed extreme points

Abstract

In this paper, we consider the mean curvature flow with driving force on fixed extreme points in the plane. We give a general local existence and uniqueness result of this problem with $C^2$ initial curve. For a special family of initial curves, we classify the solutions into three categories. Moreover, in each category, the asymptotic behavior is given.

References in corpus (1)

• Uniqueness and existence of spirals moving by forced mean curvature motion