Energy decay of a variable-coefficient wave equation with memory type acoustic boundary conditions
type: Item
instance of: scholarly article
title: Energy decay of a variable-coefficient wave equation with memory type acoustic boundary conditions
zbMATH Open document ID: 1335.35011
author: Jieqiong Wu
author: Fei Feng
author: Shengjia Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-11-10T00:00:00Z
review text: An initial boundary value problem for the homogeneous wave equation with variable coefficients in a bounded domain of \(\mathbb R^n\) modeling the evolution of the sound in a compressible fluid is investigated. A part of the boundary surface is modeled as a non-dissipative portion and on the other part the so called acoustic boundary conditions involving an integral term are introduced. Under usual conditions for the initial data and some special assumptions regarding the entries in the boundary data, the well-posedness of the stated problem is assured. Then, for the solution of this problem the corresponding energy could be defined. The main result of the paper consist in proving an estimation for this energy, the energy decay. For the proof, one makes use of the Riemannian geometry method.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 93B27
zbMATH DE Number: 6506832
zbMATH Keywords: Riemannian geometry method
zbMATH Keywords: sound in a compressible fluid
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.09.039
OpenAlex ID: W1771592624
cites work: Asymptotic Stability and Energy Decay Rates for Solutions of the Wave Equation with Memory in a Star-Shaped Domain
cites work: Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term
cites work: Exponential decay of non-linear wave equation with a viscoelastic boundary condition
cites work: Q4089240
cites work: Q4098118
cites work: Acoustic boundary conditions
cites work: Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary.
cites work: Uniform stabilization of the damped Cauchy--Ventcel problem with variable coefficients and dynamic boundary conditions
cites work: Boundary stabilization of wave equations with variable coefficients and memory.
cites work: Boundary stabilization of wave equations with variable coefficients.
cites work: Uniform Stabilization for a Hyperbolic Equation with Acoustic Boundary Conditions in Simple Connected Domains
cites work: Wave equation with porous nonlinear acoustic boundary conditions generates a well-posed dynamical system
cites work: Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions
cites work: On the wave equation with semilinear porous acoustic boundary conditions
cites work: On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback
cites work: Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
cites work: Inverse/observability estimates for second-order hyperbolic equations with variable coefficients
cites work: Well-posedness and uniform decay rates for the Klein–Gordon equation with damping term and acoustic boundary conditions
cites work: Q4276447
cites work: Q4530278
cites work: Well-posedness for a variable-coefficient wave equation with nonlinear damped acoustic boundary conditions
cites work: Uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions
cites work: Stabilization of wave equation with variable coefficients by nonlinear boundary feedback
cites work: Uniform decay of the solution to a wave equation with memory conditions on the boundary
cites work: On The Observability Inequalities for Exact Controllability of Wave Equations With Variable Coefficients
cites work: Observability inequalities for the Euler-Bernoulli plate with variable coefficients
cites work: Observability Inequalities for Shallow Shells
cites work: Global smooth solutions for the quasilinear wave equation with boundary dissipation
cites work: Boundary controllability for the quasilinear wave equation
cites work: Energy decay for the Cauchy problem of the linear wave equation of variable coefficients with dissipation
cites work: Q3173251
cites work: Global Smooth Solutions of the Quasi-Linear Wave Equation with Internal Velocity Feedback
Wikidata QID: Q125989959
DOI: 10.1016/J.JMAA.2015.09.039
description: scientific article; zbMATH DE number 6506832