An Example of Exact Solution to the Problem of Two Immiscible Liquids Filtration in a Poroelastic Medium

The paper presents the examples of exact solutions for two-phase filtration model of immiscible incompressible liquids in a poroelastic medium. Such model is used to simulate the geophysics of snow and ice covers and the magma movement in the earth's core (for gas and oil production cases). Examples of exact solutions are important when studying systems of differential equations because it is much easier to study their physical aspects. They are also useful for developing and testing the numerical algorithms. At the moment, there are quite few examples of exact solutions for the considered model. This is due to the novelty and complexity of the underlying system of differential equations. The first example is a stationary solution that is supported by excluding the effects of gravity, capillary jump, and movement at the boundaries. The corresponding environment dynamics of the solution is physical, which means no change of the main environment properties over time. The second example is the exact classic self-similar solution with a property of a finite speed phenomenon propagation associated with its physical aspect.