关于一类曲线收缩流的保积性和能量衰减性的研究

On the Area-Preserving and Energy-Decaying Properties for a Class of Curve Shortening Flows

对一类带接触角的曲线收缩流的性质进行了研究。利用Garcke和Novick-Cohen的能量定义,证明了其具有保积性和能量衰减性。稳态解在能量达到最小值时取得。

The properties of a class of curve shortening flows with contact angle is studied. With the energy defined by Garcke and Novick-Cohen, it is proved that they have the area-preserving and energy-decaying properties. The stationary solution is achieved at the minimal energy.