Wave processes in saturated porous elastic deformable media

In terms of metric strain tensor equations are given for the motion of liquids in a containing deformable frame. An equation is derived for condition of a medium without assumption of local additivity of entropy. Convertible hydrodynamic approximation is studied and propagation of small deviations from thermodynamically balanced state. The system of equations for sonic fluctuations of a two-speed hydrodynamic system is proved to be hyperbolic. The mentioned approximation in the system has three types of fluctuations: transverse sound and two lengthwise sounds. A theoretical example is developed, that describes a two-speed continuum with one pressure value. This example's equations in convertible approximation also prove to be hyperbolic. Numerically studied are transients in the non-linear two-speed hydrodynamics.