A family of evolution equations connecting area-preserving to length-preserving curve flows

摘要

In this paper we define a one parameter family of curve flows in the plane connecting a type of area-preserving to length-preserving curve flows. When the initial curve is closed and convex, we show that along the flows the length of the curve is non increasing while the enclosed area is non-decreasing. We show that the solutions exist for all time and converge to a circle in C-0 norm when t - +infinity. (C) 2018 Elsevier Ltd. All rights reserved.y