Homogenization in domains randomly perforated along the boundary

Gregory A. Chechkin; Tatiana P. Chechkina; Ciro D’Apice; Umberto De Maio

doi:10.3934/dcdsb.2009.12.713

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2009, Volume 12, Issue 4: 713-730. Doi: 10.3934/dcdsb.2009.12.713

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Homogenization in domains randomly perforated along the boundary

1.
Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991
2.
Department of Higher Mathematics, Moscow Engineering Physics Institute (State University), Kashirskoe sh., 31, Moscow 115409
3.
Dipartimento di Ingegneria dell’Informazione e Matematica Applicata, Università degli Studi di Salerno, Via Ponte don Melillo, 1, Fisciano (SA) 84084
4.
Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, DMA “R. Caccioppoli”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli

Received: July 31, 2008

Revised: December 31, 2008

Published: October 2009

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Abstract

We study the asymptotic behavior of the solution of the Laplace equation in a domain perforated along the boundary. Assuming that the boundary microstructure is random, we construct the limit problem and prove the homogenization theorem. Moreover we apply those results to some spectral problems.

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Mathematics Subject Classification: Primary: 35B27, 35P05; Secondary: 76M50.

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