A nonlinear beam equation
type: Item
instance of: scholarly article
title: A nonlinear beam equation
zbMATH Open document ID: 1021.35128
DOI: 10.1016/S0893-9659(01)00147-1
published in: Applied Mathematics Letters
publication date: 2003-03-10T00:00:00Z
review text: The aim of this paper is to prove the existence and uniqueness of weak solutions to a nonlinear beam equation with linear boundary and initial conditions. The nonlinear term appearing in the beam equation is \([g(w_{xx})]_{xx}\), where \(w=w(x,t)\) is the deflection, \(g\) is a given nonlinear function satisfying a local Lipschitz condition only. The presented method can be extended to a general second-order evolution system with hysteresis.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74H20
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 1878862
zbMATH Keywords: well-posedness
zbMATH Keywords: locally Lipschitz
zbMATH Keywords: nonlinear elastic systems
author: Azmy S. Ackleh
author: H. Thomas Banks
author: Gabriella A. Pintér
reviewed by: István Ecsedi
MaRDI profile type: Publication
cites work: Q4847284
cites work: Global solvability for damped abstract nonlinear hyperbolic systems
cites work: Well posedness for damped second order systems with unbounded input operators
cites work: Q4338950
cites work: Optimal Control Problems for Nonlinear Hyperbolic Distributed Parameter Systems with Damping Terms
description: scientific article; zbMATH DE number 1878862