林俊吉Lin, Chun-Chi陳柏宇Chen, Bo-Yu2019-09-052019-07-292019-09-052019http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G060540001S%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101580無中文摘要In this thesis, we study the problem on how to find an equilibrium configuration of a knotted Kirchhoff elastic rod by evolving it within the same knot class. The evolution is given by the $L^2$ gradient flow of the total energy composed of the Kirchhoff elastic energy and the Möbius knot energy. We would prove the long-time existence of smooth solutions for the gradient flow and discuss the asymptotic limit.Geometric flowsFourth-order problemKirchhoff elastic rodsGâteaux derivative of Möbius knot energyGeometric flowsFourth-order problemKirchhoff elastic rodsGâteaux derivative of Möbius knot energy