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- Title
Solvability of problems with degeneration: Imbibition of fluid in a porous medium.
- Authors
Kapranov, Yu.
- Abstract
For a degenerate system of equations such as the equations of motion of immiscible fluids in porous media, we study the solvability of an initial-boundary value problem. Using the process of capillary imbibition of a wetting fluid as an example, we study a class of self-similar solutions with degeneration on the movable boundary and on the entry into the porous layer. The considered problem can be reduced to the analysis of properties of a nonlinear operator equation. For the classical solution of the original problem, we prove existence and uniqueness theorems.
- Subjects
EQUATIONS of motion; POROUS materials; IMBIBITION (Chemistry); BOUNDARY value problems; NONLINEAR operator equations; UNIQUENESS (Mathematics)
- Publication
Differential Equations, 2016, Vol 52, Issue 5, p604
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266116050074