Abstract
The form of the equation of motion of porous media in terms of velocities, stresses and pressure as symmetric t-hyperbolic (in the sense of Friedrichs) system has been obtained.
References
[1] Dorovsky V.N., Continual theory of filtration, Sov. Geology and Geophysics, 1989, (30), 34–39. Search in Google Scholar
[2] Landau L.D. and Lifshits Ye.M., Fluid Mechanics, Pergamon Press, New York, 1989. Search in Google Scholar
[3] Blokhin A.M., Symmetrization of continuum mechanics equations, Sib. J. Diff. Eq., 1993, (2), 3-47. Search in Google Scholar
[4] Blokhin A.M., Dorovsky V.N.,Mathematical modelling in the theory of multivelocity continuum, Nova Science Publishers, Inc, New York, 1995. Search in Google Scholar
[5] Dorovsky V.N., Perepechko Yu.V., Romensky E.I., Wave processes in saturated porous elastically deformed media, Combustion, Explosion and Shock Waves, 1993, (29), 93-103. 10.1007/BF00755338Search in Google Scholar
[6] renkel Ya.I., On the theory of seismic and seismoelectric phenomena in a moist soil, J. Phys. USSR., 1944, (8), 230–241. Search in Google Scholar
[7] Biot M.A., Theory of propagation of elastic waves in fluidsaturated porous solid. I. Low-frequency range, J. Acoustical Society of America, 1956, (28), 168-178. 10.1121/1.1908239Search in Google Scholar
[8] Imomnazarov Kh.Kh., Some remarks on the Biot system (in Russian), Dokl. RAN, 2000, (373), 536-537. Search in Google Scholar
[9] Imomnazarov Kh.Kh.,Someremarks on the Biot system of equations describing wave propagation in a porous medium, Appl. Math. Lett., 2000, (13), 33-35. 10.1016/S0893-9659(99)00182-2Search in Google Scholar
[10] Imomnazarov Kh.Kh., Mikhailov A.A., Using Laguerre spectral method for solving a linear two-dimensional dynamic problem for porous media (in Russian), Sib. Zh.I.M., 2008, (11), 86-95. Search in Google Scholar
[11] Friedrichs K.O., Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math., 1954, (5), 345-392. 10.1002/cpa.3160070206Search in Google Scholar
[12] Godunov S.K., Equation of Mathematical Physics (in Russian), Moscow: Nauka, 1979. Search in Google Scholar
[13] Kostin V.I., Transformation of a hyperbolic equation to a symmetric system (in Russian), Ph.D. thesis, Novosibirsk 1981. Search in Google Scholar
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