, Stabilization for the wave equation with singular Kelvin-Voigt damping, pp.5-2018
Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim, vol.30, issue.5, pp.1024-1065, 1992. ,
Polynomial stability of operator semigroup, Math. Nachr, vol.279, pp.1425-1440, 2006. ,
Non-uniform stability for bounded semi-groups on Banach spaces, J. Evol. Equ, vol.8, issue.4, pp.765-780, 2008. ,
Optimal polynomial decay of functions and operator semigroups, Math. Ann, vol.347, issue.2, pp.455-478, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01257778
Stabilization of the wave equation with localized compensating frictional and Kelvin-Voigt dissipating mechanisms, Electron. J. Differ. Equ, vol.59, issue.2, pp.1-18, 2017. ,
Spectrum and stability for elastic systems with global or local Kelvin-Voigt damping, SIAM J. Appl. Math, vol.59, issue.2, pp.651-668, 1998. ,
On the mathematical model for linear elastic systems with analytic damping, SIAM J. Control Optim, vol.26, issue.3, pp.714-724, 1988. ,
Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces, Ann. Differ. Equ, vol.1, issue.1, pp.43-56, 1985. ,
, Algebraic and Geometric Methods in Mathematical Physics, Kaciveli, vol.19, pp.73-109, 1993.
, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués: Perturbations, Recherches en mathématiques appliquées, 1988.
Locally distributed control and damping for the conservative systems, SIAM J. Control Optim, vol.35, issue.5, pp.1574-1590, 1997. ,
Exponential decay of energy of the Euler-Bernoulli beam with locally distributed Kelvin-Voigt damping, SIAM J. Control Optim, vol.36, issue.3, pp.1086-1098, 1998. ,
Exponential decay of energy of vibrating strings with local viscoelasticity, Z. Angew. Math. Phys, vol.53, issue.2, pp.265-280, 2002. ,
Eventual differentiability of a string with local Kelvin-Voigt damping, ESAIM Control Optim. Calc. Var, vol.23, issue.2, pp.443-454, 2017. ,
Exponential stability for the wave equations with local Kelvin-Voigt damping, Z. Angew. Math. Phys, vol.57, issue.3, pp.419-432, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00117025
Characterization of polynomial decay rate for the solution of linear evolution equation, Z. Angew. Math. Phys, vol.56, issue.4, pp.630-644, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00129703
Stability of a string with local Kelvin-Voigt damping and nonsmooth coefficient at interface, SIAM J. Control Optim, vol.54, issue.4, pp.1859-1871, 2016. ,
Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback, Discrete Contin. Dyn. Syst., Ser. S, vol.9, issue.3, pp.791-813, 2016. ,
On the spectrum of C 0 -semigroups, Trans. Amer. Math. Soc, vol.284, issue.2, pp.847-857, 1984. ,
Exponential decay of solutions to hyperbolic equations in bounded domains, Indiana Univ. Math. J, vol.24, issue.1, pp.79-86, 1974. ,
A constructive method for the stabilization of the wave equation with localized Kelvin-Voigt damping, C. R. Acad. Sci. Paris, Ser. I, vol.350, issue.11, pp.603-608, 2012. ,
Exponential stability of an elastic string with local Kelvin-Voigt damping, Z. Angew. Math. Phys, vol.61, issue.6, pp.1009-1015, 2010. ,
On the lack of exponential stability for an elastic-viscoelastic waves interaction system, Nonlinear Anal., Real World Appl, vol.37, pp.387-411, 2017. ,
Polynomial decay of an elastic/viscoelastic waves interaction system, Z. Angew. Math. Phys, vol.69, issue.4, p.88, 2018. ,