Decay of solutions for a mixture of thermoelastic one dimensional solids

We study a PDE system modeling thermomechanical deformations for a mixture of thermoelastic solids. In particular we investigate the asymptotic behavior of the solutions. First, we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent. Subsequently, we find the necessary and sufficient conditions to guarantee the exponential decay of solutions. When the decay is not of exponential type, we prove that the solutions decay polynomially and we find the optimal polynomial decay rate