Longtime behavior of multidimensional wave equation with local Kelvin–Voigt damping

In this paper, the longtime behavior of a coupled multidimensional elastic–viscoelastic waves system is considered. This model consists of an elastic wave domain and an viscoelastic wave domain, connecting by a common interface. The dissipative damping is produced in the viscoelastic wave via the boundary connection. By the resolvent estimate together with microlocal analysis argument, we show that the corresponding semigroup is polynomially stable with decay rate (Formula presented.) under certain conditions.