Eventual differentiability of a string with local Kelvin–Voigt damping

Abstract

In this paper, we study a wave equation with local Kelvin–Voigt damping, which models one-dimensional wave propagation through two segments consisting of an elastic and a viscoelastic medium. Under the assumption that the damping coefficients change smoothly near the interface, we prove that the semigroup corresponding to the system is eventually differentiable.