Homogenization of variational inequalities and equations defined by pseudomonotone operators
Gennadiy V. Sandrakov · Sbornik Mathematics · 2008
Results on the convergence of sequences of solutions of non-linear equations and variational inequalities for obstacle problems are proved. The variational inequalities and equations are defined by a non-linear, pseudomonotone operator of the second order with periodic, rapidly oscillating coefficients and by sequences of functions characterizing the obstacles and the boundary conditions. Two-scale and macroscale (homogenized) limiting problems for such variational inequalities and equations are obtained. Results on the relationship between solutions of these limiting problems are established and sufficient conditions for the uniqueness of solutions are presented. Bibliography: 25 titles.