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Homogenization of a Boundary-Value Problem with Varying type of Boundary Conditions in a Thick Two-Level Junction

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Nonlinear Oscillations

Abstract

We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ω ɛ that is the union of a domain Ω0 and a large number 2N of thin rods with thickness of order ɛ = \(\mathcal{O}\) (N −1). Depending on their lengths, the thin rods are divided into two levels. In addition, the rods from each level are ɛ-periodically alternated. Inhomogeneous Neumann boundary conditions are given on the vertical sides of the thin rods of the first level, and homogeneous Dirichlet boundary conditions are given on the vertical sides of the rods of the second level. We investigate the asymptotic behavior of a solution of this problem as ɛ → 0 and prove a convergence theorem and the convergence of the energy integral.

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  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    T. A. Mel'nyk & P. S. Vashchuk

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  1. T. A. Mel'nyk
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  2. P. S. Vashchuk
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__________

Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 241–257, April–June, 2005.

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Mel'nyk, T.A., Vashchuk, P.S. Homogenization of a Boundary-Value Problem with Varying type of Boundary Conditions in a Thick Two-Level Junction. Nonlinear Oscill 8, 240–255 (2005). https://doi.org/10.1007/s11072-005-0053-3

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  • DOI: https://doi.org/10.1007/s11072-005-0053-3

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