Stabilization of transmission system of Kirchhoff plate and wave equations with a localized Kelvin–Voigt damping

Abstract

In this paper, we consider the stabilization for the Kirchhoff plate and equations connected by transmission conditions. We show that the energy of the transmission system is stable with logarithmic decay rate when feedback control acts on the small part of the plate as a viscoelastic material with Kelvin–Voigt constitutive relation. The proof is based on a new resolvent estimate by using some careful analysis for Kirchhoff plate-wave transmission system.