Smoothness of Local Solutions for the 4th-Order Elastic Flow of Inextensible Plane Curves

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2016

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In this paper we establish the smooth short time existence of the inextensible elastic flow, provided that our initial plane curves is $C^{3+\alpha}$. We consider two cases of initial plane curves: closed curves and open curves with hinged end. The inextensible elastic flow of such plane curves correspond to semi-linear fourth-order parabolic equations.

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非延伸性, 彈性流, 彎曲能, 平面曲線, Inextensibility, Elastic flow, Bending energy, Plane curve

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