Liu, Kangsheng; Rao, Bopeng Exponential stability for the wave equations with local Kelvin-Voigt damping. (English) Zbl 1114.35023 Z. Angew. Math. Phys. 57, No. 3, 419-432 (2006). Let \(\Omega \subset \mathbb R^N\) be a bounded open set with Lipschitz boundary. The following wave equation with local viscoelastic damping distributed around the boundary is considered \[ \rho (x)u_{tt}(x, t) = \text{div}(a(x)\nabla u + b(x)\nabla u_t)\quad (x\in\Omega,\;t>0). \] This equation involving a constructive viscoelastic damping \(\operatorname{div} b(x)\nabla u_t\), models the vibrations of an elastic body which has one part made of viscoelastic material. For the considered equation the exponential stability conditions are established. Reviewer: Michael I. Gil’ (Beer-Sheva) Cited in 3 ReviewsCited in 45 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 93D20 Asymptotic stability in control theory 35B37 PDE in connection with control problems (MSC2000) 35B35 Stability in context of PDEs 35L70 Second-order nonlinear hyperbolic equations Keywords:local viscoelastic damping; exponential energy decay; damping around the boundary PDFBibTeX XMLCite \textit{K. Liu} and \textit{B. Rao}, Z. Angew. Math. Phys. 57, No. 3, 419--432 (2006; Zbl 1114.35023) Full Text: DOI