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International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v4.i5-6.10
pages 545-558

Asymptotic Approximation of the Solution to the Robin Problem in a Thick Multistructure

C. D'Apice
Department of Information Engineering and Applied Mathematics University of Salerno, via Ponte Don Melillo, 84084 Fisciano (SA), Italia
U. De Maio
Department of Applied Mathematics "R. Caccioppoli", Federico II University of Naples, Complesso Monte S. Angelo - Edificio "T", Via Cintia, 80126 Naples, Italy
Taras A. Mel'nik
Faculty of Mathematics & Mechanics, Taras Shevchenko University of Kyiv, Volodymyrska str. 64, 01033 Kyiv, Ukraine


We consider a mixed boundary value problem for the Poisson equation in a thick multistructure Ωε, which is the union of a domain Ω0 and a large number N of ε-periodically situated thin rings with variable thickness of order ε = O(N−1). The Robin conditions are given on the lateral boundaries of the thin rings. The leading terms of the asymptotic expansion for the solution are constructed and the corresponding estimates in the Sobolev space H1ε) are proved (as ε 0) with minimal conditions for the right-hand side.

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