Strong lower energy estimates for nonlinearly damped Timoshenko beams and Petrowsky equations
type: Item
instance of: scholarly article
title: Strong lower energy estimates for nonlinearly damped Timoshenko beams and Petrowsky equations
zbMATH Open document ID: 1241.34068
author: Fatiha Alabau-Boussouira
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2011-11-30T00:00:00Z
review text: The author establishes strong lower energy estimates for strong solutions of nonlinearly damped Timoshenko beams, Petrowsky equations in two and three dimensions and wave-like equations for bounded one-dimensional domains or annulus domains in two or three dimensions. Weak lower velocity estimates for strong solutions of the nonlinearly damped Petrowsky equation are also established. In a previous paper [J. Differ. Equations 249, No. 5, 1145--1178 (2010; Zbl 1201.35042)], the author showed that it is possible to derive strong lower energy estimates for general dampings, localized as well as boundary dampings under weaker regularity assumptions on the initial data. The weak lower velocity estimates of Haraux are also extended to general dampings and multidimensional domains for bounded velocities in time and spaces.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L90
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 5982607
zbMATH Keywords: Timoshenko beams
zbMATH Keywords: wave equation
zbMATH Keywords: Petrowsky equation
zbMATH Keywords: nonlinear dissipation
zbMATH Keywords: boundary damping
zbMATH Keywords: locally distributed feedback
zbMATH Keywords: hyperbolic equations
zbMATH Keywords: optimality
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: lower energy estimates
zbMATH Keywords: regularity
zbMATH Keywords: energy comparison principles
MaRDI profile type: Publication
full work available at URL: s00030-011-0108-3
OpenAlex ID: W2094979936
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DOI: 10.1007/S00030-011-0108-3
description: scientific article; zbMATH DE number 5982607