This paper studies a class of second order partial differential equations *utt = f(ux)uxx + g(ut)* arising in poroelasticity theory with arbitrary functions *f(ux)* and *g(ut)*, using the group classification. It is shown that the principal Lie algebra of...

A modified version of the linear poroelasticity theory described by three elastic parameters is applied to shale swelling with an aqueous electrolyte. It is assumed that the shale behaves as an isotropic, ideal ionic membrane, and in this case, swelling depends only on the total stress and on the chemical...

A chemically inert deformable rock is considered, taking into account only changes in stress and pore pressure: the chemistry of a porous fluid has no direct effect on deformation. Accounting the chemical effects leads to changes in the pore pressure and in the strain of rocks. This theory is applied...

The deformation tensor *ε* in a porous medium is a function of the
stress tensor *σ* and the pore pressure *ρ*. Additional osmotic effects are present
in some rocks, such as shales. It is shown that such effects, in turn, modify the
thermodynamics of the system, namely, in terms...

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.

Mean value relations for a vector of displacement of an elastic porous body and a pore pressure for a poroelastic static system, when mass forces and energy dissipation are absent, are obtained.