Incremental equations for pre-stressed compressible viscoelastic materials

In this paper, we face the question of describing the incremental motion of pre-stressed isotropic homogeneous compressible viscoelastic materials of differential type. We obtain a set of linear evolution equations which generalizes the previous mathematical description of the problem. Well-posedeness of the associated Cauchy problems and dissipation properties are established as well. In the final part, a reduction to a unique equation of the sixth order is derived, and a physical example is exhibited.