A thermodynamically consistent system of conservation laws for the flow of a compressible fluid in an elastic porous medium

Basing on the method of thermodynamically consistent systems of conservation laws we develop a model of the isoentropic flow of a compressible fluid in an elastically deformable porous medium in the case of finite deformations, whose defining equations are hyperbolic and has divergence form. We also derive equations for the propagation of small amplitude waves in a motionless medium and analyze the dependence of the speed of sound on porosity.