On a one- dimensional model of the finite elastostatics
type: Item
instance of: scholarly article
title: On a one- dimensional model of the finite elastostatics
zbMATH Open document ID: 0759.73020
DOI: 10.4171/ZAA/440
author: A. Langenbach
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1992-08-13T00:00:00Z
review text: Summary: The deformation of a \(\text{rod }S=[0,1]\) is given by a diffeomorphism \(w: S\to S_ w=[0,w(1)]\) from the set \(\{w\in W^ 2_ 2(0,1): w(0)=0, w'(s)>0 (s\in S)\}\). The function \(\ln w'\) appears as measure of deformation. The function \(w\) is solution to a second order ordinary differential equation with the second boundary condition \(w'(1)=p\in\mathbb{R}^ +\). By an open-and-closed argument we show that the set of those \(p\) for which the boundary problem is uniquely solvable, is all \(\mathbb{R}^ +\).
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 40551
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: boundary value problems
zbMATH Keywords: second order ordinary differential equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 40551