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

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