Okabe, Shinya The motion of elastic planar closed curves under the area-preserving condition. (English) Zbl 1121.74009 Indiana Univ. Math. J. 56, No. 4, 1871-1912 (2007). Summary: We consider the motion of an elastic closed curve with constant enclosed area. This motion is governed by a system involving fourth-order parabolic equations. We prove that this system has a unique classical solution for all time, and that the solution converges uniformly to a stationary solution together with its derivatives of any order. Cited in 1 ReviewCited in 18 Documents MSC: 74B99 Elastic materials 74G65 Energy minimization in equilibrium problems in solid mechanics Keywords:fourth-order parabolic equations; unique solution; bending energy; uniform convergence PDFBibTeX XMLCite \textit{S. Okabe}, Indiana Univ. Math. J. 56, No. 4, 1871--1912 (2007; Zbl 1121.74009) Full Text: DOI Link