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Homogenization of a parabolic signorini boundary value problem in a thick plane junction

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We consider a parabolic Signorini boundary value problem in a thick plane junction Ω ε which is the union of a domain Ω0 and a large number of ε−periodically situated thin rods. The Signorini conditions are given on the vertical sides of the thin rods. The asymptotic analysis of this problem is done as ε → 0, i.e., when the number of the thin rods infinitely increases and their thickness tends to zero. With the help of the integral identity method we prove a convergence theorem and show that the Signorini conditions are transformed (as ε → 0) in differential inequalities in the region that is filled up by the thin rods in the limit passage. Bibliography: 31 titles. Illustrations: 1 figure.

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Authors and Affiliations

  1. National Taras Shevchenko University of Kyiv, 64, Volodymyrska St., Kyiv, 01033, Ukraine

    T. A. Mel’nyk & Iu. A. Nakvasiuk

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  1. T. A. Mel’nyk
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  2. Iu. A. Nakvasiuk
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Correspondence to T. A. Mel’nyk.

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Translated from Problemy Matematicheskogo Analiza, 63, January 2012, pp. 67–82.

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Mel’nyk, T.A., Nakvasiuk, I.A. Homogenization of a parabolic signorini boundary value problem in a thick plane junction. J Math Sci 181, 613–631 (2012). https://doi.org/10.1007/s10958-012-0708-4

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