Well-Posedness and Stabilizability of a Viscoelastic Equation in Energy Space

DOI10.2307/2154987zbMath0809.45009OpenAlexW4233760094MaRDI QIDQ4316954

Olof J. Staffans

Publication date: 19 December 1994

Full work available at URL: https://doi.org/10.2307/2154987

zbMATH Keywords

Hilbert spacewell-posednesslinear viscoelasticityenergy spaceexponential stabilizabilityabstract Volterra integrodifferential system

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Abstract integral equations, integral equations in abstract spaces (45N05) Dynamical problems in solid mechanics (74Hxx)

Related Items (17)

Hamiltonian and Lagrangian theory of viscoelasticity ⋮ Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions ⋮ Optimal control for stochastic Volterra equations with multiplicative Lévy noise ⋮ Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach ⋮ An analytic semigroup setting for a class of Volterra equations ⋮ On a mathematical framework for the constitutive equations of anisotropic dielectric relaxation ⋮ Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications ⋮ Volterra series for solving weakly non-linear partial differential equations: application to a dissipative Burgers’ equation ⋮ Controllability of a class of Volterra equations in Hilbert spaces with completely monotone kernel ⋮ Efficient solution of a wave equation with fractional-order dissipative terms ⋮ Asymptotic stability of linear conservative systems when coupled with diffusive systems ⋮ Asymptotic stability of Webster-Lokshin equation ⋮ Mesoscopic Modeling of Stochastic Reaction-Diffusion Kinetics in the Subdiffusive Regime ⋮ Diffusive Approximation of a Time-Fractional Burger's Equation in Nonlinear Acoustics ⋮ Passive boundary damping of viscoelastic structures ⋮ Stress obtained by interpolation methods for a boundary value problem in linear viscoelasticity ⋮ A concept of energy Banach space and its application to the gradient method

Cites Work

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• A decomposition method for integro-partial differential equations and applications
• Fractional derivatives and smoothing in nonlinear conservation laws
• On the Spectrum of C 0 -Semigroups
• Singular Relaxation Moduli and Smoothing in Three-Dimensional Viscoelasticity
• Spectral Theory for Contraction Semigroups on Hilbert Space
• Evolutionary Integral Equations and Applications

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