CONVERGENCE THEOREMS FOR SOLUTIONS AND ENERGY FUNC- TIONALS OF BOUNDARY VALUE PROBLEMS IN THICK MULTILEVEL JUNCTIONS OF A NEW TYPE WITH PERTURBED NEUMANN CON- DITIONS ON THE BOUNDARY OF THIN RECTANGLES

摘要

Boundary value problems for the Poisson equation are considered in a multilevel thick junction consisting of a junction body and a lot of alternating thin rectangles of two levels depending on their lengths. Rectangles of the first level have a finite length, whereas rectangles of the second level have a length ε~α, 0 < α < 1, where e is the alternation period. On the boundary of thin rectangles, an inhomogeneous Neumann boundary condition involving additional perturbation parameters is imposed. We prove convergence theorems for solutions and energy integrals. Regarding the convergence of solutions of the original problem to solutions of the homogenized problem, we establish some (auxiliary) estimates necessary for obtaining the convergence rate.