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

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

張育瑋(Chang Yu-Wei)

指導教授 ： 林俊吉

國立臺灣師範大學/理學院/數學系/碩士(2016年)

https://doi.org/10.6345/NTNU202204555

摘要

無中文摘要

關鍵字

非延伸性 ； 彈性流 ； 彎曲能 ； 平面曲線

並列摘要

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.

並列關鍵字

Inextensibility ； Elastic flow ； Bending energy ； Plane curve

參考文獻

A. Ferrero, F. Gazzola, H.-Ch. Grunau. Decay and eventual local positivity for biharmonic parabolic equations. In Disc. Cont. Dynam. Syst. 21, 2008, 1129-1157.

V.A. Galaktionov, S.I. Poho zaev. Existence and blow-up for higher-order semilinear parabolic equations: majorizing order-preserving operators. In Indiana Univ. Math. J. 51, 2002, 1321-1338.

N. V. Krylov. Lectures on Elliptic and Parabolic Equations in Holder spaces. In Amer. Math. Soci., Graduate Studies in Mathematics Volume 12, 1996.

N. Koiso. On the motion of a curve towards elastica. In Actes da la Table Ronde de G eometrie Di erentielle (Luminy 1992), S emin Congr. 1 Soc. Math. France, Paris, 1996, 403-436.

V. Solonnikov. On the boundary value problems for linear parabolic systems of di erential equations of general form. In Proc. Steklov Inst. Math, volume 83, pages 1-162, 1965.