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Mat. Sb., 2001, Volume 192, Number 2, Pages 87–102 (Mi msb544)  

This article is cited in 11 scientific papers (total in 11 papers)

Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain

S. E. Pastukhova

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: For the case of a 2-connected $\varepsilon$-periodic $(\varepsilon\in(0,1))$ perforated space with a bounded domain $\Omega_\varepsilon$ selected in it the homogenization property as $\varepsilon\to0$ is proved for the boundary-value problem for a second-order elliptic operator in the domain $\Omega_\varepsilon$ with one-sided condition of Signorini type on the boundaries of “cavities” and with Dirichlet condition on the outer boundary.

DOI: https://doi.org/10.4213/sm544

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English version:
Sbornik: Mathematics, 2001, 192:2, 245–260

Bibliographic databases:

UDC: 517.953
MSC: 35B27, 35J15
Received: 24.04.2000

Citation: S. E. Pastukhova, “Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain”, Mat. Sb., 192:2 (2001), 87–102; Sb. Math., 192:2 (2001), 245–260

Citation in format AMSBIB
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\pages 87--102
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pastukhova S.E., “The oscillating boundary phenomenon in the homogenization of a climatization problem”, Differ. Equ., 37:9 (2001), 1276—-1283  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. I. I. Argatov, “Osrednenie smeshannoi zadachi dlya operatora Laplasa s usloviyami Sinorini na vnutrennei melkozernistoi granitse”, Sib. zhurn. industr. matem., 7:4 (2004), 3–15  mathnet  mathscinet  zmath
    3. Sandrakov G.V., “Homogenization of variational inequalities with the Signorini condition in perforated domains”, Dokl. Math., 70:3 (2004), 941–944  mathnet  mathscinet  mathscinet  isi
    4. G. V. Sandrakov, “Homogenization of variational inequalities for non-linear diffusion problems in perforated domains”, Izv. Math., 69:5 (2005), 1035–1059  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Kazmerchuk Yu.A., Mel'nyk T.A., “Homogenization of the signorini boundary-value problem in a thick plane junction”, Nonlinear Oscill., 12:1 (2009), 45–59  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. T. A. Mel'nyk, Iu. A. Nakvasiuk, W. L. Wendland, “Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem”, Math. Meth. Appl. Sci, 2010, n/a  crossref  mathscinet  isi  scopus  scopus  scopus
    7. Sango M., “Homogenization of the Neumann Problem for a Quasilinear Elliptic Equation in a Perforated Domain”, Networks and Heterogeneous Media, 5:2 (2010), 361–384  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    8. T. A. Mel’nyk, Iu. A. Nakvasiuk, “Homogenization of a parabolic signorini boundary value problem in a thick plane junction”, J Math Sci, 2012  crossref  mathscinet  scopus  scopus  scopus
    9. Amirat Y., Shelukhin V.V., “Homogenization of composite electrets”, Eur. J. Appl. Math., 28:2 (2017), 261–283  crossref  mathscinet  zmath  isi  scopus
    10. Gomez D., Lobo M., Perez E., Podolskii V A., Shaposhnikova T.A., “Unilateral Problems For the P-Laplace Operator in Perforated Media Involving Large Parameters”, ESAIM-Control OPtim. Calc. Var., 24:3 (2018), 921–964  crossref  isi  scopus
    11. Ptashnyk M., “Homogenization of Some Degenerate Pseudoparabolic Variational Inequalities”, J. Math. Anal. Appl., 469:1 (2019), 44–75  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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