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International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

Institutional price:	$747.00
Issues per year:	6

Best Paper Award Selection - Editorial Board Site

2006, Volume4

271 pages

DOI: 10.1615/IntJMultCompEng.v4.i5-6

Issue price - $256.00

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

ABSTRACT

We consider a mixed boundary value problem for the Poisson equation in a thick multistructure Ω_ε, 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 H¹ (Ω_ε) are proved (as ε → 0) with minimal conditions for the right-hand side.