On the control of a viscoelastic damped Timoshenko-type system

In this paper we consider the following Timoshenko systemφtt-(φx+ψ)x=0,(0,1)×(0,+∞)ψtt-ψxx+∫0tg(t-τ)ψxx(τ)dτ+φx+ψ=0,(0,1)×(0,+∞)with Dirichlet boundary conditions where gg is a positive nonincreasing function. We establish an exponential and polynomial decay results with weaker conditions on gg than those required in [F. Ammar-Khodja, A. Benabdallah, J.E. Muñoz Rivera, R. Racke, Energy decay for Timoshenko systems of memory type, J. Differ. Equations, 194 (2003) 82–115].