LEADER 03232nam 2200505 450 001 996490343603316 005 20231110214936.0 010 $a3-031-12519-3 035 $a(CKB)5850000000078717 035 $a(MiAaPQ)EBC7101908 035 $a(Au-PeEL)EBL7101908 035 $a(PPN)264953576 035 $a(EXLCZ)995850000000078717 100 $a20230224d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStabilization of Kelvin-Voigt damped systems /$fKai?s Ammari and Fathi Hassine 210 1$aCham, Switzerland :$cBirkha?user,$d[2022] 210 4$dŠ2022 215 $a1 online resource (156 pages) 225 1 $aAdvances in Mechanics and Mathematics ;$vv.47 311 $a3-031-12518-5 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- Contents -- 1 Preliminaries -- 1.1 Semigroups of Bounded Linear Operators -- 1.1.1 Basic Properties -- 1.2 Stability -- 1.2.1 Strong Stability -- 1.2.2 Exponential Stability -- 1.2.3 Polynomial Stability -- 1.2.4 Logarithmic Stability -- 2 Stability of Elastic Transmission Systems with a Local Kelvin-Voigt Damping -- 2.1 Introduction -- 2.2 Transversal Motion -- 2.3 Longitudinal Motion -- 3 Stabilization for the Wave Equation with Singular Kelvin-Voigt Damping -- 3.1 Introduction and Main Results -- 3.2 Well-posedness and Strong Stability -- 3.3 Carleman Estimate -- 3.4 Stabilization Result -- 4 Logarithmic Stabilization of the Euler-Bernoulli Transmission Plate Equation with Locally Distributed Kelvin-Voigt Damping -- 4.1 Introduction -- 4.2 Model and Statement of Results -- 4.3 Existence and Uniqueness -- 4.4 Carleman Estimate and Construction of the Weight Functions -- 4.4.1 Carleman Estimate -- 4.4.2 Construction of the Weight Functions -- 4.5 Resolvent Estimate -- 5 Energy Decay Estimates of Elastic Transmission Wave/Beam Systems with a Local Kelvin-Voigt Damping -- 5.1 Introduction and Motivation -- 5.2 Preliminary and Main Results -- 5.3 Damping Arising from the Transversal Motion -- 5.4 Damping Arising from the Longitudinal Motion -- 5.5 Non-exponential Stability -- 5.5.1 Case When the Damping Arising from the Wave Equation -- 5.5.2 Case When the Damping Arising from the Beam Equation -- 6 Asymptotic Behavior of the Transmission Euler-Bernoulli Plate and Wave Equation with a Localized Kelvin-Voigt Damping -- 6.1 Introduction -- 6.1.1 The Method of Analysis -- 6.2 Existence and Uniqueness -- 6.3 Carleman Estimate Near the Surface -- 6.4 Resolvent Estimate -- 7 Conclusion and Perspectives -- References. 410 0$aAdvances in Mechanics and Mathematics 606 $aDamping (Mechanics) 606 $aEstabilitat$2thub 606 $aMecānica$2thub 608 $aLlibres electrōnics$2thub 615 0$aDamping (Mechanics) 615 7$aEstabilitat 615 7$aMecānica 676 $a534.42 700 $aAmmari$b Kai?s$0716377 702 $aHassine$b Fathi 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996490343603316 996 $aStabilization of Kelvin-Voigt damped systems$93030310 997 $aUNISA