November  2009, 12(4): 713-730. doi: 10.3934/dcdsb.2009.12.713

Homogenization in domains randomly perforated along the boundary

1. 

Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, Russian Federation

2. 

Department of Higher Mathematics, Moscow Engineering Physics Institute (State University), Kashirskoe sh., 31, Moscow 115409, Russian Federation

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  August 2008 Revised  January 2009 Published  August 2009

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.
Citation: Gregory A. Chechkin, Tatiana P. Chechkina, Ciro D’Apice, Umberto De Maio. Homogenization in domains randomly perforated along the boundary. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 713-730. doi: 10.3934/dcdsb.2009.12.713
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