Stability of elastic transmission systems with a local Kelvin-Voigt damping

DOI10.1016/j.ejcon.2015.03.001zbMath1360.93600arXiv1812.05923OpenAlexW2038483708MaRDI QIDQ522778

Fathi Hassine

Publication date: 19 April 2017

Published in: European Journal of Control (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05923

zbMATH Keywords

wave equationstabilizationEuler-Bernoulli beam equationtransmission problemelastic systemslocal Kelvin-Voigt damping

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Asymptotic stability in control theory (93D20) Wave equation (35L05)

Related Items (21)

A transmission problem of a system of weakly coupled wave equations with Kelvin-Voigt dampings and non-smooth coefficient at the interface ⋮ Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping ⋮ Polynomial decay rate of C₀ semigroup in Hilbert spaces ⋮ Stability of a Graph of Strings with Local Kelvin–Voigt Damping ⋮ Stabilization of a 1-D transmission problem for the Rayleigh beam and string with localized frictional damping ⋮ Stabilization for vibrating plate with singular structural damping ⋮ Stability of an infinite star‐shaped network of strings by a Kelvin–Voigt damping ⋮ Stability for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping ⋮ Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin–Voigt damping ⋮ Stability for coupled waves with locally disturbed Kelvin-Voigt damping ⋮ Stability results of a singular local interaction elastic/viscoelastic coupled wave equations with time delay ⋮ Logarithmic stabilization of the Euler-Bernoulli transmission plate equation with locally distributed Kelvin-Voigt damping ⋮ On the stability of Bresse system with one discontinuous local internal Kelvin-Voigt damping on the axial force ⋮ Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients ⋮ Stability of a star-shaped network with local Kelvin-Voigt damping and non-smooth coefficient at interface ⋮ Stabilization of transmission system of Kirchhoff plate and wave equations with a localized Kelvin-Voigt damping ⋮ Uniform stability of transmission of wave-plate equations with source on Riemannian manifold ⋮ Stabilization for the wave equation with singular Kelvin-Voigt damping ⋮ Stability of the wave equations on a tree with local Kelvin-Voigt damping ⋮ Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping. ⋮ Stability results for an elastic–viscoelastic wave equation with localized Kelvin–Voigt damping and with an internal or boundary time delay

Cites Work

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• Stabilization of a system modeling temperature and porosity fields in a Kelvin-Voigt-type mixture
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• Characterization of polynomial decay rate for the solution of linear evolution equation
• Exponential stability for the wave equations with local Kelvin-Voigt damping
• On the Spectrum of C 0 -Semigroups
• Spectral Theory for Contraction Semigroups on Hilbert Space
• Spectrum and Stability for Elastic Systems with Global or Local Kelvin--Voigt Damping
• Exponential Decay of Energy of the Euler--Bernoulli Beam with Locally Distributed Kelvin--Voigt Damping
• Equivalent Norms for Sobolev Spaces

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