\(L^ 2\) flow of curve straightening in the plane
type: Item
instance of: scholarly article
title: \(L^ 2\) flow of curve straightening in the plane
zbMATH Open document ID: 0815.58020
DOI: 10.1215/S0012-7094-93-07016-0
author: Yingzhong Wen
published in: Duke Mathematical Journal
publication date: 1995-07-11T00:00:00Z
review text: For a plane curve considered as an elastic wire, the time evolution is modeled by decreasing total squared curvature. The resulting model is a partial differential equation \(u_ t = u_{ss} + f(u)\) with boundary conditions. Long time existence of solutions is established. Moreover, it is shown that convex curves stay convex and that a curve with rotation number \(\eta \neq 0\) approaches an \(\eta\)-fold circle.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 558980
zbMATH Keywords: curve straightening flow
zbMATH Keywords: evolution equation
zbMATH Keywords: convex curve
zbMATH Keywords: total squared curvature
zbMATH Keywords: rotation number
reviewed by: Dieter Erle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 558980