On the wave equation with semilinear porous acoustic boundary conditions

DOI10.1016/j.jde.2012.01.042zbMath1250.35135OpenAlexW1969175151MaRDI QIDQ413449

Philip Jameson Graber, Belkacem Said-Houari

Publication date: 7 May 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2012.01.042

zbMATH Keywords

exponential growthenergy decayacoustic wavenonlinear semigroup theory

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Variational methods applied to PDEs (35A15) Wave equation (35L05) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions
• Decay rate estimates for wave equations of memory type with acoustic boundary conditions
• Exact controllability of structural acoustic interactions
• Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction
• Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping
• Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping
• Wave equation with porous nonlinear acoustic boundary conditions generates a well-posed dynamical system
• Compact sets in the space \(L^ p(0,T;B)\)
• Decay estimates for some semilinear damped hyperbolic problems
• Stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions
• Sharp regularity theory for second order hyperbolic equations of Neumann type. I: \(L_ 2\) nonhomogeneous data
• Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. II: General boundary data
• Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions
• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation
• Boundary stabilization of a 3-dimensional structural acoustic model
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Global nonexistence theorems for quasilinear evolution equations with dissipation
• Polynomial decay for the energy with an acoustic boundary condition
• Some nonlinear wave equations with acoustic boundary conditions
• Uniform decay properties of a model in structural acoustics
• Development of singularities in solutions of a hyperbolic system
• Global nonexistence theorems for a class of evolution equations with dissipation
• Oscillatory boundary conditions for acoustic wave equations
• Exact controllability of finite energy states for an acoustic wave/plate interaction under the influence of boundary and localized controls
• Problèmes unilateraux
• Global existence for the wave equation with nonlinear boundary damping and source terms
• Global non-existence of solutions of a class of wave equations with non-linear damping and source terms
• Acoustic boundary conditions
• REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
• The wave equation with semilinear Neumann boundary conditions
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Exponential Decay Rates for Structural Acoustic Model with an Overdamping on the Interface and Boundary Layer Dissipation
• ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION
• Uniform Stabilization for a Hyperbolic Equation with Acoustic Boundary Conditions in Simple Connected Domains
• Abstract wave equations with acoustic boundary conditions
• Equivalent Norms for Sobolev Spaces
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations

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