On the existence of global solution of the system of equations of one-dimensional motion of a viscous liquid in a deformable viscous porous medium

The initial-boundary value problem for the system of one-dimensional motion of a viscous liquid in a deformable viscous porous medium is considered. Local theorem of existence and uniqueness of the problem is proved in the case of compressible liquid. In the case of incompressible liquid the theorem of global solvability in time is proved in Holder classes.