Asymptotic expansion for a solution of an elliptic boundary-value problem in a thin cascade domain

Abstract

Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin cascade domain. Asymptotic energetic and uniform pointwise estimates for the difference between the solution of the initial problem and the solution of the corresponding limiting problem are proved.

23 pages, 5 figures