Stability and Regularity of Solution to the Timoshenko Beam Equation with Local Kelvin--Voigt Damping

DOI10.1137/17M1146506zbMath1415.35184OpenAlexW2899304021WikidataQ129006412 ScholiaQ129006412MaRDI QIDQ4553298

Qiong Zhang, Zhuangyi Liu

Publication date: 2 November 2018

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1146506

zbMATH Keywords

eventual differentiabilityexponential and polynomial stabilityinterface of the damped and undamped regionlocally distributed Kelvin-Voigt damping

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) One-parameter semigroups and linear evolution equations (47D06) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items (9)

Polynomial stability for a Timoshenko-type system of thermoelasticity with partial Kelvin-Voigt damping ⋮ Stability analysis of a Timoshenko beam with local degenerate viscoelastic damping ⋮ Effects of Kelvin-Voigt damping on the stability of (thermo)elastic Timoshenko system with second sound ⋮ Sharp stability of a string with local degenerate Kelvin–Voigt damping ⋮ Energy decay of a mixture with local viscoelasticity ⋮ Well-posedness and energy decay for some thermoelastic systems of Timoshenko type with Kelvin-Voigt damping ⋮ A transmission problem for the Timoshenko system with one local Kelvin-Voigt damping and non-smooth coefficient at the interface ⋮ Stabilization of Wave Equation on Cuboidal Domain via Kelvin--Voigt Damping: A Case without Geometric Control Condition ⋮ Explicit decay rate for a degenerate hyperbolic-parabolic coupled system

Cites Work

• Unnamed Item
• Lack of exponential stability to Timoshenko system with viscoelastic Kelvin-Voigt type
• Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system
• Exponential stability of an elastic string with local Kelvin-Voigt damping
• The stability number of the Timoshenko system with second sound
• Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks
• Optimal polynomial decay of functions and operator semigroups
• On the stability of damped Timoshenko systems: Cattaneo versus Fourier law
• Semigroups of linear operators and applications to partial differential equations
• Weighted Hardy inequality
• Uniform decay rates for the energy of Timoshenko system with the arbitrary speeds of propagation and localized nonlinear damping
• Stability to 1-D thermoelastic Timoshenko beam acting on shear force
• A localized nonstandard stabilizer for the Timoshenko beam
• Stability of a Timoshenko system with local Kelvin-Voigt damping
• Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control
• Characterization of polynomial decay rate for the solution of linear evolution equation
• Polynomial stability of the Timoshenko system by one boundary damping
• Stability for the Timoshenko beam system with local Kelvin-Voigt damping
• Eventual differentiability of a string with local Kelvin–Voigt damping
• On localized Kelvin-Voigt damping
• Stability of a String with Local Kelvin--Voigt Damping and Nonsmooth Coefficient at Interface
• Stabilization of the uniform Timoshenko beam by one locally distributed feedback
• Exponential Decay of Energy of Evolution Equations with Locally Distributed Damping
• General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping
• On the Spectrum of C 0 -Semigroups
• Boundary Control of the Timoshenko Beam
• 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

This page was built for publication: Stability and Regularity of Solution to the Timoshenko Beam Equation with Local Kelvin--Voigt Damping