A theory of porous thermoviscoelastic mixtures

In this article we derive a theory for binary mixtures of viscoelastic bodies. The individual components of the mixture are modelled as porous Kelvin-Voigt viscoelastic materials. First, the basic equations of the nonlinear theory of heat conducting viscoelastic mixtures are derived in lagrangian description. A frame independent nonlinear constitutive relation which generalizes the Darcy's law is derived. Then, the theory is linearized and a uniqueness result is presented. Finally, an exponential decay estimate of the solutions is established.