Exponential stabilization of the Timoshenko system by a thermal effect with an oscillating kernel

In this paper, we consider a Timoshenko system supplemented by a heat equation with a viscoelastic damping term. We prove an exponential decay of solutions under weak assumptions. The kernels we consider here are weaker than the ones used usually in viscoelasticity. This kind of thermal damping was first introduced by Rivera and Racke (2002) [1] and then modified according to the Green and Naghdi theory (Green and Naghdi (1991, 1992) [2] and [3]) by the present authors, Djebabla and Tatar (2010) [4].