Abstract
We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ℝ2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.
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This work was supported by Postdoctoral Science Foundation of China, National Natural Science Foundation of China (No. 10631020, 10871061) and the Grant for PhD Program of Ministry of Education of China
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Liu, Y., Jian, H. A curve flow evolved by a fourth order parabolic equation. Sci. China Ser. A-Math. 52, 2177–2184 (2009). https://doi.org/10.1007/s11425-009-0143-2
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DOI: https://doi.org/10.1007/s11425-009-0143-2