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Izvestiya: Mathematics, 2005, Volume 69, Issue 5, Pages 1035–1059
DOI: https://doi.org/10.1070/IM2005v069n05ABEH002287
(Mi im660)
 

This article is cited in 14 scientific papers (total in 14 papers)

Homogenization of variational inequalities for non-linear diffusion problems in perforated domains

G. V. Sandrakov

National Taras Shevchenko University of Kyiv
References:
Abstract: We consider the homogenization of non-linear diffusion problems with various boundary conditions in periodically perforated domains. These problems are stated as variational inequalities defined by non-linear strictly monotone operators of second order with periodic rapidly oscillating coefficients. We establish the relevant convergence of solutions of the problems to solutions of two-scale and macroscale limiting variational inequalities. We give methods for deriving such limiting variational inequalities. In the case of potential operators, we establish relations between the limiting variational inequalities obtained and the two-scale and macroscale constrained minimization problems.
Received: 17.05.2004
Bibliographic databases:
UDC: 517.95
MSC: 35B27
Language: English
Original paper language: Russian
Citation: G. V. Sandrakov, “Homogenization of variational inequalities for non-linear diffusion problems in perforated domains”, Izv. Math., 69:5 (2005), 1035–1059
Citation in format AMSBIB
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\by G.~V.~Sandrakov
\paper Homogenization of variational inequalities for non-linear diffusion problems in perforated domains
\jour Izv. Math.
\yr 2005
\vol 69
\issue 5
\pages 1035--1059
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  • https://doi.org/10.1070/IM2005v069n05ABEH002287
  • https://www.mathnet.ru/eng/im/v69/i5/p179
  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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