Polynomial decay rate for a wave equation with general acoustic boundary feedback laws
type: Item
instance of: scholarly article
title: Polynomial decay rate for a wave equation with general acoustic boundary feedback laws
zbMATH Open document ID: 1275.35034
author: Yanyan Li
published in: S\(\vec{\text{e}}\)MA Journal
publication date: 2013-04-08T00:00:00Z
review text: This paper is concerned the stabilization of the wave equation by a general class of acoustic boundary feedback laws at one extremity. This system is not uniformly stable, but the authors furnish sufficient conditions that guarantee a polynomial stability. Their method combines the use of an observability inequality for the associated undamped problem obtained via sharp spectral results with regularity results of the solution of the undamped problem with a specific right-hand side. In some particular cases, the optimality of the decay is shown again with the help of precise spectral results of the operator associated with the damped problem. They also illustrate the general results by some examples.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 93B07
zbMATH DE Number: 6151336
zbMATH Keywords: observability inequality
MaRDI profile type: Publication
full work available at URL: s40324-013-0002-5
OpenAlex ID: W2162642354
cites work: Stabilization of Bernoulli--Euler beams by means of a pointwise feedback force
cites work: Tauberian Theorems and Stability of One-Parameter Semigroups
cites work: Ingham-Beurling type theorems with weakened gap conditions
cites work: Q4442410
cites work: On the Stabilization of a Flexible Beam with a Tip Mass
cites work: On the Spectral Properties and Stabilization of Acoustic Flow
cites work: Q3193115
cites work: A dynamic control law for the wave equation
cites work: Polynomial decay for the energy with an acoustic boundary condition
cites work: Stabilization of the wave equation on 1-D networks with a delay term in the nodal feedbacks
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Stabilization of Elastic Plates with Dynamical Boundary Control
cites work: Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods
cites work: Controllability and Stabilizability of the Third-Order Linear Dispersion Equation on a Periodic Domain
cites work: Rational energy decay rate for a wave equation with dynamical control
DOI: 10.1007/S40324-013-0002-5
description: scientific article; zbMATH DE number 6151336