Global Solvability of a System of Equations of One-Dimensional Motion of a Viscous Fluid in a Deformable Viscous Porous Medium

Abstract

The mathematical statement is given for the problem of filtration of a viscous fluid in a deformable porous medium that possesses predominantly viscous properties. Some theorems are proved on local solvability and existence of a global-in-time solution in the Hölder classes for the problem.