ASYMPTOTIC EXPANSION OF THE SOLUTION OF AN ELLIPTIC BOUNDARY-VALUE PROBLEM IN A THIN CASCADE DOMAIN

摘要

We construct and substantiate an asymptotic expansion for the solution of an inhomogeneous Neumann boundary-value problem for the Poisson equation whose right-hand side depends on longitudinal and transverse variables in a thin cascade domain. We find the asymptotic energy and establish uniform pointwise estimates for the difference between the solution of the original problem and the solution of the corresponding limit problem.