On travelling waves in a suspension bridge model as the wave speed goes to zero
type: Item
instance of: scholarly article
title: On travelling waves in a suspension bridge model as the wave speed goes to zero
zbMATH Open document ID: 1228.34065
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-06-14T00:00:00Z
review text: The authors are concerned with finding homoclinic solutions to the equation \[ y'''+ c^2 y''+ (1+ y)^+- 1= 0,\tag{\(*\)} \] which are related to travelling wave solutions with speed \(c\) to \(u_{tt}+ u_{xxxx}+ u^+= 1\). They prove that as \(c\to 0\), all solutions of \((*)\) tend to \(+\infty\) in the \(L^\infty\)-norm.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 5907674
zbMATH Keywords: nonlinear beam
zbMATH Keywords: suspension bridgesep
zbMATH Keywords: travelling waves
author: Alan C. Lazer
author: P. Joseph Mckenna
MaRDI profile type: Publication
full work available at URL: j.na.2011.03.024
OpenAlex ID: W2082472061
cites work: Nonlinear oscillations in a suspension bridge
cites work: Travelling Waves in a Suspension Bridge
cites work: Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
cites work: Travelling waves in a nonlinearly suspended beam: some computational results and four open questions
cites work: Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
cites work: The existence of ground states for fourth-order wave equations
cites work: Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations
cites work: A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam
cites work: Homoclinic Solutions for Fourth Order Traveling Wave Equations
cites work: Solitary waves in nonlinear beam equations: Stability, fission and fusion
DOI: 10.1016/J.NA.2011.03.024
Recommended article: A lower bound for the amplitude of traveling waves of suspension bridges
Recommended article: Traveling Waves in a Suspension Bridge System
Recommended article: Travelling Waves in a Suspension Bridge
Recommended article: Multibump periodic travelling waves in suspension bridges
Recommended article: Multiple periodic solutions to a suspension bridge wave equation with damping
Recommended article: Q4672309
Recommended article: Asymptotic behaviour of a suspension bridge problem
Recommended article: Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
Recommended article: On solitary waves of a piecewise linear suspended beam model
Recommended article: Travelling waves in a nonlinearly suspended beam: some computational results and four open questions
description: scientific article; zbMATH DE number 5907674