On a non-local curve evolution problem in the plane

This paper deals with a new curvature flow for closed convex plane curves which shortens the length of the evolving curve but expands the area it bounds and makes the evolving curve more and more circular during the evolution process. And the final shape of the evolving curve will be a circle (as the time t goes to infinity). This flow is determined by a coupled system concerning both local and global geometric quantities of the evolving curve.

2010 Mathematics Subject Classification

35K15, 35K65, 53A04

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Published 1 January 2008