Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin–Voigt damping

DOI10.1080/00207179.2015.1135509zbMath1364.35043arXiv1812.05924OpenAlexW3104547590MaRDI QIDQ2979526

Fathi Hassine

Publication date: 25 April 2017

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

Full work available at URL: https://arxiv.org/abs/1812.05924

zbMATH Keywords

wave equationstabilisationtransmission problembeam equationpolynomial decayelastic systems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35) Asymptotic stability in control theory (93D20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for higher-order hyperbolic systems (35L57)

Related Items (18)

A transmission problem of a system of weakly coupled wave equations with Kelvin-Voigt dampings and non-smooth coefficient at the interface ⋮ Regularity and asymptotic behavior for a damped plate-membrane transmission problem ⋮ Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping ⋮ Polynomial stability of transmission viscoelastic wave and plate equations on Riemannian manifolds ⋮ Stabilization of a 1-D transmission problem for the Rayleigh beam and string with localized frictional damping ⋮ Stabilization for weakly coupled string–riser system with partial frictional damping ⋮ Stability for an interface transmission problem of wave-plate equations with dynamical boundary controls ⋮ Stability for Euler-Bernoulli beam equation with a local degenerated 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 ⋮ Exponential stability of a damped beam-string-beam transmission problem ⋮ 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 ⋮ Stabilization of transmission system of Kirchhoff plate and wave equations with a localized Kelvin-Voigt damping ⋮ Stabilization for the wave equation with singular 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

• Energy decay estimates for some weakly coupled Euler-Bernoulli and wave equations with indirect damping mechanisms
• Stability of elastic transmission systems with a local Kelvin-Voigt damping
• Stabilization of a system modeling temperature and porosity fields in a Kelvin-Voigt-type mixture
• Long-time behavior of a coupled heat-wave system arising in fluid-structure interaction
• Optimal polynomial decay of functions and operator semigroups
• Stabilization of a transmission wave/plate equation
• Semigroups of linear operators and applications to partial differential equations
• The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system
• Control, observation and polynomial decay for a coupled heat-wave system
• Decay rates for the three-dimensional linear system of thermoelasticity
• Characterization of polynomial decay rate for the solution of linear evolution equation
• Polynomial decay for a hyperbolic-parabolic coupled system
• The strong stability and instability of a fluid-structure semigroup
• Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
• Polynomial stability of operator semigroups
• A Note on Weak Stabilizability of Contraction Semigroups
• 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
• Indirect Boundary Stabilization of Weakly Coupled Hyperbolic Systems

This page was built for publication: Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin–Voigt damping