Geometric theory of special modes in the distributed-parameter control systems. I

The present paper is the first in the projected series of publications illustrating the application of the geometric theory of singular solutions of the nonlinear partial differential equations to the description of special modes in the distributed-parameter control systems. Consideration was given to the problem of biphase unidimensional filtering of fluids (oil and water) in the porous media of the natural oil pools.
The paper is an extended version of the report presented at the International Conference PACO'2012 prepared for publication on recommendation of the Program Committee [1].

Presented by the member of Editorial Board: A. P. Krishchenko