Energy decay for a coupled wave system with one local Kelvin–Voigt damping

Abstract

In this paper, we study the energy decay of a coupled wave system with one local Kelvin–Voigt damping. The system consists of two wave equations locally coupled by zero‐order terms. When the damping coefficient function and the coupling coefficient function satisfy suitable assumptions, by Carleman estimate and the frequency‐domain method, we show that the energy of the system decays logarithmically for sufficiently smooth initial data.