Small perturbations of two-phase thermofluid in pores: linearization procedure and equations of isothermal microstructure

We consider the most general dynamical model describing the joint motion of a heat-conductive elastic porous body and a two-phase heat-conductive Newtonian viscous compressible fluid. We assume that the fluid fills in the whole porous space. Since the fluid in pores and the solid composing the pore space are distinguished and at the same time we think of pores that they have very small diameters but their aggregate capacity is significant with the respect to the entire fluid-solid bulk, the considered model corresponds to microstructure. In the present article the linearization procedure is fulfilled on a natural rest state by means of the classical formalism. On the base of the obtained linearized model, a simplified isothermal formulation is set up and the existence and uniqueness theory is built for it. The proofs are based on the classical methods in the theory of evolutionary partial differential equations.