Energy convergence results for strongly damped nonlinear wave equations
type: Item
instance of: scholarly article
title: Energy convergence results for strongly damped nonlinear wave equations
zbMATH Open document ID: 0603.35065
DOI: 10.1007/BF01179262
author: Joel D. Arvin
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173858
review text: Let A, B be (unbounded) positive self-adjoint operators on a Hilbert space H. Consider the strongly-damped nonlinear wave equation (SDNWE) \[ u_{tt}+(\alpha A^ 2+\beta)u_ t+B^ 2u=F(u) \] where \(\alpha\), \(\beta\) are nonnegative constants and F is a nonlinear map. We develop criteria under which solutions of the SDNWE converge in a suitable energy norm to a solution of the undamped equation \((\alpha =\beta =0)\) on closed time intervals [0,T]. In our application, the vibrating beam equation, T can be chosen arbitrarily large.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 3973448
zbMATH Keywords: positive self-adjoint operators
zbMATH Keywords: Hilbert space
zbMATH Keywords: strongly-damped nonlinear wave equation
zbMATH Keywords: energy norm
zbMATH Keywords: undamped equation
zbMATH Keywords: vibrating beam
MaRDI profile type: Publication
cites work: Nonlinear second order equations with applications to partial differential equations
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cites work: Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis
cites work: Higher Order Estimates and Smoothness of Nonlinear Wave Equations
OpenAlex ID: W1987212453
description: scientific article; zbMATH DE number 3973448