In this paper we consider a one-dimensional linear thermoelastic system of Timoshenko type with past history acting only in one equation. We consider the model where the heat conduction is given by Green and Naghdi's theories and prove exponential and polynomial stability results for the equal and nonequal wave-speed propagation. Our results are established under conditions on the relaxation function weaker than those in .
"Energy decay in a Timoshenko-type system with history in thermoelasticity of type III." Adv. Differential Equations 14 (3/4) 375 - 400, MArch/April 2009.