Uniform stabilization for the transmission problem of the Timoshenko system with memory

Abstract

In this paper we study the transmission for a partially viscoelastic beam, that is, a beam which is composed of two components, elastic and viscoelastic. In the rotation angle of the filaments of the beam, ψ1(x,t) and ψ2(x,t), the dissipation is occasioned by the memory effect. In the transverse vibrations ϕ1(x,t) and ϕ2(x,t) we do not have dissipation and the system is purely elastic. For this type of beam we show the uniform stabilization, i.e., the rate of decay has directly relation with the velocity of the relaxation function.