Rybalko V. Homogenized models with memory

Double porosity type models, vibrations of elastic media with concentrated masses. To construct homogenized models. Methods used are methods of homogenization theory, methods of functional analysis, theory of functions of complex variable, spectral theory of selfadjoint operators. The diffusion model, whose tensor of coefficients of diffusion degenerates on a set of asymptotically full measure, is investigated, a homogenized model with memory is obtained; a double porosity type model for reaction-diffusion equation is studied, the two-scale homogenized problem is obtained; the model of vibrations of elastic media with a large number of heavy rigid inclusions is investigated, the homogenized model of vibrations is obtained. The results and the methods developed could be used in further investigations of physical processes in strongly inhomogeneous media.