Memory‐type boundary stabilization of a transmission problem for Kirchhoff wave equations

Abstract

In this paper, we consider a transmission problem for Kirchhoff‐type wave equations with boundary condition determined by the long‐range memory. The wave propagation over bodies consisting of two physically different types of materials. One component is clamped, and the other is in a viscoelastic fluid producing a dissipative mechanism on the boundary. Under a wider assumption of the kernel, we establish a more general decay rate of energy, which improves earlier results established in the literature.