Some developments of the homogenization theory and related questions

Abstract: This thesis is mainly devoted to homogenization theory and it consists of an introduction, five papers and two conference proceedings. The introduction gives an elementary presentation of the basic ideas in homogenization theory, serves as an overview of the field and points out where the results of this thesis fit in. A short description of the Rothe method is also included in the introduction. The first paper deals with reiterated homogenization of degenerate nonlinear monotone operators. In the second paper bounds and some numerical results for the homogenized degenerated p- Poisson equation are given. The third and fourth paper are devoted to stochastic homogenization where the third deals with random degenerated nonlinear monotone operators and the fourth with an approximation model, namely periodic approximaton, for elasticity properties of random media. In the fifth paper the Rothe method is generalized to the case with parabolic equations on non-cylindrical domains. In the last two papers some numerical aspects of the homogenization theory are investigated.