Decay rates of the solution of the Cauchy thermoelastic Bresse system

We consider two Cauchy problems for the one-dimensional thermoelastic Bresse model. Using the energy method in the Fourier space, we show that for the first model, the \({L^{2}}\)-norm of the solution decays with the rate \({(1+t)^{-1/12}}\). In addition, the same decay rate has been obtained for the second model.