Exponential and polynomial stability of a wave equation for boundary memory damping with singular kernels

DOI10.1016/j.crma.2009.01.005zbMath1175.35012OpenAlexW2031125701MaRDI QIDQ1009532

Fatiha Alabau-Boussouira, Rico Zacher, Jan W. Prüss

Publication date: 2 April 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.01.005

zbMATH Keywords

boundary feedbackmultiplier methodpolynomial delaymethod of higher order energies

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35)

Related Items (15)

Energy decay rates for solutions of the Kirchhoff type wave equation with boundary damping and source terms ⋮ Preface. Special issue dedicated to Jan Prüss on the occasion of his 65th birthday ⋮ Exponential stability of a certain semigroup and applications ⋮ Asymptotics of solutions to a system of connected incomplete second-order integro-differential operator equations ⋮ General decay for the degenerate equation with a memory condition at the boundary ⋮ Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions ⋮ Boundary stabilization for axially moving Kirchhoff string under fractional PI control ⋮ Well-posedness and asymptotic behavior of a nonautonomous, semilinear hyperbolic-parabolic equation with dynamical boundary condition of memory type ⋮ A Katznelson-Tzafriri theorem for measures ⋮ Integro-differential equations of hyperbolic type with positive definite kernels ⋮ Stabilization through viscoelastic boundary damping: a semigroup approach ⋮ A general method for proving sharp energy decay rates for memory-dissipative evolution equations ⋮ Energy decay estimates of solutions for viscoelastic damped wave equations in \(\mathbb{R}^N\) ⋮ Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions ⋮ Energy decay rates for a hyperbolic differential inclusion with viscoelastic boundary conditions

Cites Work

• Indirect internal stabilization of weakly coupled evolution equations
• Maximal regularity of type \(L_p\) for abstract parabolic Volterra equations
• Convergence to equilibrium for second order differential equations with weak damping of memory type
• On the existence and the asymptotic stability of solutions for linearly viscoelastic solids
• On wave equations with boundary dissipation of memory type
• Decay estimates for second order evolution equations with memory
• Lyapunov functions and convergence to steady state for differential equations of fractional order
• An abstract Volterra equation with applications to linear viscoelasticity
• Asymptotic stability in viscoelasticity
• Asymptotic stability of wave equations with memory and frictional boundary dampings
• Stabilisation frontière indirecte de systèmes faiblement couplés
• Asymptotic behaviour of the energy in partially viscoelastic materials
• Frictional versus Viscoelastic Damping in a Semilinear Wave Equation
• Indirect Boundary Stabilization of Weakly Coupled Hyperbolic Systems
• Lyapunov functionals for reaction-diffusion equations with memory
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