A curvature flow in the plane with a nonlocal term
We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time asymptotics of this flow.
Mathematics Subject Classification35K10 53A04
Hui Yu would like to thank many colleagues and friends, in particular Hongjie Dong, Dennis Kriventsov and Tianling Jin, for fruitful discussions concerning this project, especially for the discussion about parabolic equations in one spatial dimension. He is also grateful to Yanyan Li and Jingang Xiong for their invitation to Beijing Normal University, where part of this work was conducted.
- 5.Yu, H.: Motion of sets by curvature and derivative of capacity potential, preprintGoogle Scholar