Application of $A$-analytic functions to the investigation of the Cauchy problem for a stationary poroelasticity system
Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 65 (2019) no. 1, pp. 33-43.

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In a reversible hydrodynamic approximation, a closed system of second-order dynamic equations with respect to the displacement vector of an elastic porous body and pore pressure has been obtained. The Cauchy problem for the obtained system of poroelasticity equations in the stationary case is considered. The Carleman formula for the Cauchy problem under consideration has been constructed.
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Kh. Kh. Imomnazarov; N. M. Jabborov. Application of $A$-analytic functions to the investigation of the Cauchy problem for a stationary poroelasticity system. Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 65 (2019) no. 1, pp. 33-43. http://geodesic.mathdoc.fr/item/CMFD_2019_65_1_a3/

[1] L. A. Aizenberg, Formuly Karlemana v kompleksnom analize, Nauka, Novosibirsk, 1990 (in Russian) | MR

[2] E. V. Arbuzov, “The Cauchy problem for second-order elliptic systems on a plane”, Sib. Math. J., 44:1 (2003), 3–20 (in Russian) | MR | Zbl

[3] A. V. Bitsadze, Some Classes of Partial Differential Equations, Nauka, M., 1981 (in Russian)

[4] A. L. Bukhgeym, Introduction to the Theory of Inverse Problems, Nauka, Novosibirsk, 1988 (in Russian) | MR

[5] I. N. Vekua, New Methods for Solving of Elliptic Equations, OGIZ, M., 1948 (in Russian) | MR

[6] I. N. Vekua, Generalized Analytic Functions, Nauka, M., 1988 (in Russian)

[7] I. E. Niezov, “The Cauchy problem for a system of the elasticity theory on a plane”, Uzbek Math. J., 1996, no. 1, 27–34 (in Russian) | MR

[8] R. S. Saks, Boundary-Value Problems for Systems of Elliptic Equations, NGU, Novosibirsk, 1975 (in Russian)

[9] A. P. Soldatov, “Higher-order elliptic systems”, Differ. Equ., 25:1 (1989), 136–144 (in Russian) | MR | Zbl

[10] A. P. Soldatov, One-Dimensional Singular Operators and Boundary-Value Problems of the Elasticity Theory, Vysshaya shkola, M., 1991 (in Russian)

[11] N. E. Tovmasyan, “General boundary-value problem for second-order elliptic systems with constant coefficients”, Differ. Equ., 2:2 (1966), 163–171 (in Russian) | MR

[12] Ya. I. Frenkel', “To the theory of seismic and seismoelectrical phenomena in a moist soil”, Bull. Acad. Sci. USSR. Ser. Geograph. Geophys., 8:4 (1944), 133–150 (in Russian) | Zbl

[13] Arbuzov E. V., Bukhgeim A. L., “Carleman's formulas for $A$-analytic functions in a half-plane”, J. Inverse Ill-Posed Probl., 5:6 (1997), 491–505 | DOI | MR | Zbl

[14] Bers L., Theory of pseudo-analytic functions, Lecture Notes, N.Y., 1953 | MR | Zbl

[15] Biot M. A., “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range”, J. Acoust. Soc. Am., 28:2 (1956), 168–178 | DOI | MR

[16] Bitsadze A. V., Boundary value problems for second-order elliptic equations, North-Holland, Amsterdam, 1968 | MR | Zbl

[17] Blokhin A. M., Dorovsky V. N., Mathematical modelling in the theory of multivelocity continuum, Nova Science, New York, 1995 | MR

[18] Bonnet G., “Basic singular solutions for a poroelastic medium in the dynamic range”, J. Acoust. Soc. Am., 82 (1987), 1758–1762 | DOI

[19] Dorovsky V. N., Perepechko Yu. V., Romensky E. I., “Wave processes in saturated porous elastically deformed media”, Combustion, Explosion and Shock Waves, 29:1 (1993), 93–103 | DOI

[20] Giraud G., “Nouvelles methode pour traiter certaines problemes relatifs aux equations du type elliptique”, J. de Math., 18 (1939), 111–143 | MR

[21] Gorog S., Panneton R., Atalla N., “Mixed displacement-pressure formulation for acoustic anisotropic open porous media”, J. Appl. Phys., 82 (1997), 4192–4196 | DOI

[22] Imomnazarov Kh. Kh., “Some remarks on the Biot system of equations describing wave propagation in a porous medium”, Appl. Math. Lett., 13:3 (2000), 33–35 | DOI | MR | Zbl

[23] Lavrentiev M. M., Some improperly posed problems in mathematical physics, Springer, Berlin, 1967