MODELING OF WAVE PROCESSES IN POROUS MEDIA AND ASYMPTOTIC EXPANSIONS
Abstract
Models of wave processes in porous periodic media are considered. It is taken into account that the corresponding wave equations depend on small parameters characterizing the microscale, density, and permeability of such media. The algorithm for determining asymptotic expansions for these equations is given. Estimates for the accuracy of such expansions are presented.
References
Bensoussan A., Lions J.-L., and Papanicolau G. Asymptotic analysis for periodic structures. North-Holland, Amsterdam 1978.
Bakhvalov N. S., Panasenko G. P. Homogenization: averaging processes in periodic media. Kluwer, Dordrecht 1989.
Sandrakov G. V. The homogenization of nonstationary equations with contrast coefficients. Doklady Mathematics.1997. Vol. 56:1. P. 586–589.
Sandrakov G. V. Homogenization of elasticity equations with contrasting coefficients. Sbornik: Mathematics.1999. Vol. 190:12. P. 1749–1806. https://doi.org/10.1070/SM1999v190n12ABEH000443
Sandrakov G. V. Multiphase models of nonstationary diffusion in homogenization. Comput. Math. Math. Phys. 2004. Vol. 44: 10. P. 1741–1756.
Sandrakov G. V. Multiphase homogenized diffusion models for problems with several parameters. Izvestiya: Mathematics. 2007. Vol. 71: 6. P. 1193–1252. https://doi.org/10.1070/IM2007v071n06ABEH002387
Agranovich M. S., Vishik M. I. Elliptic problems with a parameter and parabolic problems of general type. Russian Math. Surveys. 1964. Vol. 19: 3. P. 53–157. https://doi.org/10.1070/RM1964v019n03ABEH001149
Sandrakov G. V. Averaging principles for equations with rapidly oscillating coefficients. Mathematics of the USSR - Sbornik.1991. Vol. 68: 2. P. 503–553. https://doi.org/10.1070/SM1991v068n02ABEH002111
Duvaut G., Lions J.-L. Les inequations en mecanique et en physique. Dunod, Paris 1972.
Mitrea M., Taylor M. Boundary layer methods for Lipschitz domains in Riemannian manifolds. J. Functional Analysis.1999. Vol. 163: 2. P. 181–251. https://doi.org/10.1006/jfan.1998.3383