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 Tr. Mat. Inst. Steklova, 2005, Volume 250, Pages 105–111 (Mi tm34)

This article is cited in 3 scientific papers (total in 3 papers)

Homogenized Tensor on Networks

V. V. Zhikova, S. E. Pastukhovab

a Vladimir State Pedagogical University
b Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: The homogenized tensor that arises in problems of elasticity theory on periodic networks is studied. On the basis of the relaxation formula, optimal networks are described for which the homogenized tensor can be determined in an explicit form, exact calculations for some nonoptimal networks are performed, and the nondegeneracy properties of the homogenized tensor are investigated. Scalar problems are handled similarly; the class of optimal networks for them proves to be larger than that for problems of elasticity theory.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 250, 95–101

Bibliographic databases:

UDC: 517.9
Received in January 2005

Citation: V. V. Zhikov, S. E. Pastukhova, “Homogenized Tensor on Networks”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 250, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 105–111; Proc. Steklov Inst. Math., 250 (2005), 95–101

Citation in format AMSBIB
\Bibitem{ZhiPas05} \by V.~V.~Zhikov, S.~E.~Pastukhova \paper Homogenized Tensor on Networks \inbook Differential equations and dynamical systems \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2005 \vol 250 \pages 105--111 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm34} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200911} \zmath{https://zbmath.org/?q=an:1138.74380} \transl \jour Proc. Steklov Inst. Math. \yr 2005 \vol 250 \pages 95--101 

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This publication is cited in the following articles:
1. S. E. Pastukhova, “Homogenization of elasticity problems on periodic composite structures”, Sb. Math., 196:7 (2005), 1033–1073
2. Cardone G., Pastukhova S.E., Perugia C., “Estimates in Homogenization of Degenerate Elliptic Equations by Spectral Method”, Asymptotic Anal., 81:3-4 (2013), 189–209
3. V. V. Zhikov, G. A. Yosifian, “Introduction to the theory of two-scale convergence”, J. Math. Sci. (N. Y.), 197:3 (2014), 325–357
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