Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference "Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

On new inverse problems for the pseudoparabolic equations of filtration in fissured media

A fissured rock is considered as a material consisting of pores and permeable blocks which are generally separated from each other by a system of fissures. Compared to the standard arguments of filtration in a porous medium the significant feature of the concept lies in the fact that 1) two liquid pressures, both in the pores and in the fissures, are introduced at any point in a space and 2) the transfer of liquids between the fissures and the pores is taken into consideration. Under such an approach the model of the seepage of a liquid in a fissured rock is described by the so-called fissured medium equation (the linear pseudoparabolic equation of the third order). More general model can include the nonlinearities arising from fluid type (liquid or gas), concentration (porosity, absorption or saturation) and the exchange rate. Since the natural stratum is involved, the parameters in the equation should be determined on the basis of the investigation of their behavior under the natural nonsteady-state conditions but not the artificial tests in a laboratory. This leads to the interest in studying the inverse problems for such equation and its analogue.

Pseudoparabolic equations with various differential operators of the even order in spacial variables also arise in the mathematical models of the diffusion, the heat conduction and wave processes, in the models for filtration in porous media with the dynamic capillary pressure.
This investigation is devoted to the new inverse problems concerning the identification of coefficients in the second and third order terms of linear pseudoparabolic equation of filtration in a fissured rock. The coefficients depend on the permeability and hydraulic properties of the fissured rock. The coefficient of the third order term involves the intensity of the liquid transfer between the blocks and fissures and represents the specific characteristic of the fissured rock.
In this report the physical and mathematical justification of possible statements of the inverse problems for pseudoparabolic equations is given. New kinds of the boundary conditions of overdetermination are discussed. Certain elliptic and parabolic inverse problems relevant to pseudoparabolic ones are considered.

 Abstracts file: thesis_lyubanova_engl_rush.rtf Full text file: lyubanova.doc

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