yusupov.pdf178.38 KB

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...

imomnazarov_0_0.pdf276.03 KB

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...

haydarov.pdf205.28 KB

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...

imomnazarov1.pdf193.69 KB

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...

imomnaz1.pdf206.16 KB

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.