Asymptotic Approximation of the Solution of the Robin Problem in a Thick Multi-structure,

We consider a mixed boundary value problem for the Poisson equation in a thick multistructure Q,, which is the union of a domain Omega(0) and a large number N of epsilon-periodically situated thin rings with variable thickness of order epsilon = O(N-1). The Robin conditions are given on the lateral boundaries of the thin rings. The leading terms of the asymptotic expansion for the solution are constructed and the corresponding estimates in the Sobolev space H-1 (Omega epsilon) are proved (as epsilon -> 0) with minimal conditions for the right-hand side