On a mixed problem with a nonlinear acoustic boundary condition for a non-locally reacting boundaries

DOI10.1016/j.jmaa.2013.05.054zbMath1310.35153OpenAlexW2024118291MaRDI QIDQ2257668

André Vicente, Cicero Lopes Frota

Publication date: 26 February 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.05.054

zbMATH Keywords

nonlinear boundary conditionLaplace-Beltrami operatornonlinear wave equationnon-locally reacting boundary

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70)

Related Items (13)

General decay estimates for the wave equation with acoustic boundary conditions in domains with nonlocally reacting boundary ⋮ Nonlinear wave equation with Dirichlet and acoustic boundary conditions: theoretical analysis and numerical simulation ⋮ Uniform stabilization of wave equation with localized damping and acoustic boundary condition ⋮ Energy decay for the wave equation of variable coefficients with acoustic boundary conditions in domains with nonlocally reacting boundary ⋮ General decay of solutions of a wave equation with memory term and acoustic boundary condition ⋮ On second-order differential equations with nonsmooth second member ⋮ On a nonlinear problem with Dirichlet and acoustic boundary conditions ⋮ Theoretical analysis and numerical simulation for a hyperbolic equation with Dirichlet and acoustic boundary conditions ⋮ On a nonlinear coupled system of thermoelastic type with acoustic boundary conditions ⋮ Uniform stabilization of wave equation with localized internal damping and acoustic boundary condition with viscoelastic damping ⋮ On Stability Equivalence between Dynamic Output Feedback and Static Output Feedback for a Class of Second Order Infinite-Dimensional Systems ⋮ The damped wave equation with acoustic boundary conditions and non-locally reacting surfaces ⋮ A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stabilization of the damped wave equation with Cauchy-Ventcel boundary conditions
• Wave equation in domains with non locally reacting boundary.
• Nonlinear wave equation with weak dissipative term in domains with non-locally reacting boundary
• Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions
• On the convergence to stationary solutions for a semilinear wave equation with an acoustic boundary condition
• Decay rate estimates for wave equations of memory type with acoustic boundary conditions
• On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms
• Asymptotic stability of the wave equation on compact manifolds and locally distributed damping: A sharp result
• Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction
• Wave equation with porous nonlinear acoustic boundary conditions generates a well-posed dynamical system
• A difference inequality and its application to nonlinear evolution equations
• Best constants in second-order Sobolev inequalities on Riemannian manifolds and applications.
• Some nonlinear wave equations with acoustic boundary conditions
• Global solvability for the quasilinear damped wave equation with nonlinear second-order boundary conditions
• Stabilization of the wave equations with potential and indefinite damping
• Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term
• Global solvability and decay of the energy for the nonhomogeneous Kirchhoff equation
• Existence of global solutions and energy decay for the Carrier equation with dissipative term
• Partial differential equations. 2: Qualitative studies of linear equations
• Global existence for the wave equation with nonlinear boundary damping and source terms
• Wave equation with damping affecting only a subset of static Wentzell boundary is uniformly stable
• Wave Equation with Acoustic/Memory Boundary Conditions
• Asymptotic stability of the wave equation on compact surfaces and locally distributed damping-A sharp result
• Acoustic boundary conditions
• Existence and uniform decay of solutions of a degenerate equation with nonlinear boundary damping and boundary memory source term
• On the non-linear vibration problem of the elastic string

This page was built for publication: On a mixed problem with a nonlinear acoustic boundary condition for a non-locally reacting boundaries