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Non-isothermal filtration and seismic acoustic in porous soils: thermo-viscoelastic and Lamé equations

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Abstract

The paper considers the linear system of differential equations describing the simultaneous motion of an incompressible elastic porous body and an incompressible fluid filling in the pores. The model considered is very complicated, since the basic differential equations contain nondifferentiable rapidly oscillating small and large coefficients under the derivative signs. On the basis of the Nguetseng two-scaled convergence, the author suggests a correct deduction of averaged equations which are either the thermo-viscoelasticity system of equations (connected pore space) or the anisotropic Lamé systemof thermoelasticity.

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Authors and Affiliations

  1. Belgorod State University, Belgorod, Russia

    A. Meirmanov

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  1. A. Meirmanov
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Correspondence to A. Meirmanov.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal Conference–2006, Part 3, 2008.

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Meirmanov, A. Non-isothermal filtration and seismic acoustic in porous soils: thermo-viscoelastic and Lamé equations. J Math Sci 160, 33–44 (2009). https://doi.org/10.1007/s10958-009-9482-3

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  • DOI: https://doi.org/10.1007/s10958-009-9482-3

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