Ukrainian Mathematical Bulletin

Volume 2, Issue 4, 2005 pp. 467-485.

Asymptotic Solution to a Mixed Boundary-Value Problem in a Thick Multi-Structure of Type 3:2:2

Authors: Umberto De Maio and Taras A. Mel'nyk
Author institution: Umberto De Maio, Department of Applied Mathematics ``R. Caccioppoli'' Federico II University of Naples, Complesso Monte S. Angelo-Edificio ``T'' Via Cintia, 80126 Naples, Italy udemaio@unina.it Taras A. Mel'nyk, Faculty of Mathematics and Mechanics Taras Shevchenko University of Kyiv, Volodymyrska str. 64, 01033 Kyiv, Ukraine melnyk@imath.kiev.ua

Summary: The leading terms of the asymptotic expansion for the solution to a mixed boundary-value problem for the Poisson equation in a thick multi-structure, which is the union of some domain and a large number~$N$ of $\varepsilon$-periodically situated thin annular disks with variable thickness of order $\varepsilon = {\cal O} (N^{-1}),$ are constructed and the corresponding estimates in the Sobolev space $H^1$ are proved as $\varepsilon\to 0.$

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