Ibrahim Aganović

Homogenization of stationary flow of miscible fluids in a domain with a grained boundary

The purpose of this paper is to obtain phenomenological equations for stationary miscible displacement in a domain with a grained boundary (porous medium), with the help of homogenization of fluid mechanics equations. It is assumed that the viscosity of the mixture depends on the concentration of the solvent.

On the stability of rotating rods and plates

In this paper use discuss the stability of straight rods and plates, rotating, respectively, around a central line and an axis, lying in the middle surface. Our purpose is to estimate (from below) the critical angular velocity, producing a transversal instability.

Homogenization of a spectral problem for a pile foundation structure

The subject of this paper is the study of free oscillations of a composite material consisting of an elastic medium and a large number of elastic piles periodically immersed in a part of the medium. The ends of piles lying on the boundary of the medium are clamped to a force-free rigid plate. Such a partially composite structure arises in pile foundation mechanics. Assuming that the period of pile structure tends to zero, we obtain the macroscopic equations for free oscillations by homogenization method and prove the corresponding convergence result.