Optimal polynomial stability of a string with locally distributed Kelvin–Voigt damping and nonsmooth coefficient at the interface

Abstract

The purpose of this paper is to investigate the stabilization of one‐dimensional wave equation with localized internal viscoelastic damping of Kelvin–Voigt type in a bounded domain. In this work, we consider only one damping Kelvin–Voigt mechanism acting in the internal of the body. Using frequency domain arguments combined with the multiplier method, we prove that the energy of the system has the optimal decay of type t−4.