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Asymptotic analysis of a boundary-value problem in a cascade thick junction with a random transmission zone

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In the article we deal with the homogenization of a boundary-value problem for the Poisson equation in a singularly perturbed two-dimensional junction of a new type. This junction consists of a body and a large number of thin rods, which join the body through the random transmission zone with rapidly oscillating boundary. Inhomogeneous Fourier boundary conditions with perturbed coefficients are set on the boundaries of the thin rods and with random perturbed coefficients on the boundary of the transmission zone. We prove the homogenization theorems and the convergence of the energy integrals. It is shown that there are three qualitatively different cases in the asymptotic behaviour of the solutions.

Keywords: homogenization; random boundary; rapidly oscillating boundary; thick junction

Document Type: Research Article


Affiliations: 1: Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lemonosov State University, Moscow, 119991 Russian Federation,Department of Applied Mathematics, Narvik University College, Narvik, 8505 Norway 2: Department of Higher Mathematics, Moscow Engineering Physics Institute (State University), Kashirskoe sh., Moscow, 115409 Russian Federation 3: Departimento di Ingegneria dell'Informazione e, Universita degli Studi di Salerno, Fisciano (SA), 84084 Italy 4: Dipartimento di Matematica e Applicazioni, Universita degli Studi di Napoli Federico II, Napoli, 80126 Italy 5: Department of Mathematical Physics, Faculty of Mechanics and Mathematics, National Taras Shevehenko University of Kyiv, Kyiv, 01033 Ukraine

Publication date: October 1, 2009

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