• G. V. Sandrakov Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Keywords: initial boundary value problems, wave equations, homogenized problems, Laplace transform


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.


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.

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.

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.

Sandrakov G. V. Averaging principles for equations with rapidly oscillating coefficients. Mathematics of the USSR - Sbornik.1991. Vol. 68: 2. P. 503–553.

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.