Sadovyi D. Asymptotic analysis of boundary-value problems in thick multi-level junctions of type 3:2:2

We study the asymptotic behavior of solutions to both linear and quasilinear elliptic and parabolic boundary-value problems in thick multi-level junctions of type 3:2:2 with various types of boundary conditions, given on the surfaces of the thin domains of a thick junction, when the number of the attached thin domains tends to infinity and their thickness tends to zero. The convergence theorems are proved, asymptotic approximations to solutions of such boundary-value problems are constructed and the corresponding estimates in Sobolev spaces are deduced. The influence of the geometric structure of a thick junction and boundary conditions on the boundaries of the thin domains on the asymptotic behavior of solutions is studied.