Thin layer of a non-Newtonian fluid flowing on a rough surface and percolating through a perforated obstacle

We study the behavior of a thin layer of a conducting dilatant fluid percolating through a porous obstacle and flowing on a rough surface. The characteristic size of pores in the obstacle (the initial velocity profile) and the roughness of the lower boundary play a role of a small parameter of order . For a family of boundary value problems depending on ε we construct a homogenized (limit) problem and prove the homogenization theorem. Thereby we describe the effective behavior of such a non-Newtonian fluid. Bibliography: 16 titles. Illustrations: 2 figures.