Global solvability of the problem of viscous fluid filtration in a viscoelastic porous medium with permeable boundaries
Global solvability of the problem of viscous fluid filtration in a viscoelastic porous medium with permeable boundaries
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 23, 1, pp. 571-581 (2026)
Abstract:
Using the theory of interacting continua, governing equations for the motion of a viscous fluid in a poroelastic skeleton were obtained. In the first stage, local solvability in Holder classes was established. Uniform time estimates were then obtained, and global solvability of the initial-boundary value problem was established.
Keywords: poroelasticity, two-phase filtration, Darcy's law, global solvability, viscoelasticity.