Bae, Jeong Ja, On uniform decay for transmission problem of Kirchhoff type viscoelastic wave equation, Acta mathematica Sinica. English series (Print) , 26(7), 2010, pp. 1197-1206
In this paper we consider the large time behavior of solutions to an n-dimensional transmission problem for two Kirchhoff type viscoelastic wave equations, that is, the wave propagation over bodies consisting of two physically different types of materials. One component is a simple elastic part while the other is a viscoelastic component endowed with a long range memory. We show that the dissipation produced by the viscoelastic part is strong enough to produce exponential or polynomial decay of the solution