Continuous dependence in a nonlinear theory of viscoelastic porous mixtures

This paper is concerned with a nonlinear theory of viscoelastic mixtures. The classical Kelvin–Voigt viscoelastic model is generalized by using a mixture theory. First, we present the basic equations in lagrangian description. We consider the volume fraction field of each constituent as an independent kinematical variable. We derive a constitutive relation which generalizes Darcy’s law. This relation is frame-independent. Then,we establish the continuous dependence of solutions upon the initial state and body loads, for mixtures which are nonconductor of heat. A uniqueness result is also presented.