We consider a one-dimensional inverse boundary value problem for a nonlinear system of the poroelasticity equations. We obtain estimates for the conditional stability of the inverse problem.

We consider a one-dimensional direct initial-boundary value problem for a nonlinear system of the poroelasticity equations. The theorem of local solvability of the classical solution to the problem is proved. The Frechet differentiability of the problem operator is proved, too.

A series of the differential identities connecting velocities, pressure and body force in the two-velocity hydrodynamics equations with equilibrium of pressure phases are found. Some of these identities have a divergent form and can be considered to be certain conservation laws. It is detected that the flow functions for the...

A flow of incompressible viscous two-velocity fluids for the case of pressure equilibrium of phases at constant saturation of substances is described with the help of scalar functions. A system of differential equations for these functions is obtained. An example illustrating this method is presented.