JournalszaaVol. 18, No. 4pp. 953–975

Homogenization of the Poisson Equation in a Thick Periodic Junction

  • T.A. Mel'nyk

    Kyiv University, Ukraine
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Abstract

A convergence theorem and asymptotic estimates as ϵ0\epsilon \to 0 are proved for a solution to a mixed boundary-value problem for the Poisson equation in a junction Ωϵ\Omega_{\epsilon}, of a domain Ω0\Omega_0 and a large number N2N^2 of ϵ\epsilon-periodically situated thin cylinders with thickness of order ϵ=O(1N)\epsilon = O(\frac{1}{N}). For this junction, we construct an extension operator and study its properties.

Cite this article

T.A. Mel'nyk, Homogenization of the Poisson Equation in a Thick Periodic Junction. Z. Anal. Anwend. 18 (1999), no. 4, pp. 953–975

DOI 10.4171/ZAA/923