Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions
type: Item
instance of: scholarly article
title: Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions
zbMATH Open document ID: 1172.35443
author: Irena Lasiecka
author: Daniel Toundykov
author: Moez Daoulatli
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2009-05-12T00:00:00Z
review text: The article refers to a mixed problem for the wave equation, on a bounded domain in a \(d\)-dimensional space, with a nonlinear boundary damping. The goal of the paper is to derive energy decay rates for this nonlinear problem. One proves estimates for different types of damping: linearly bounded near infinity, superlinear near infinity, sublinear near infinity, superlinear at infinity with a stricter regularity assumption as well as some combinations of damping at the origin and infinity. The study is based on the following technique: associate the energy functional to the nonlinear problem, start with the linear PDE problem, prove observability inequality, built an appropriate nonlinear differential equation and estimate solutions for this one.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 5552666
zbMATH Keywords: boundary damping
zbMATH Keywords: decay rates
zbMATH Keywords: observability inequality
MaRDI profile type: Publication
full work available at URL: dcdss.2009.2.67
OpenAlex ID: W2051026540
DOI: 10.3934/DCDSS.2009.2.67
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description: scientific article; zbMATH DE number 5552666