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Mat. Sb., 2008, Volume 199, Number 1, Pages 67–100 (Mi msb1116)  

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

Homogenization of variational inequalities and equations defined by pseudomonotone operators

G. V. Sandrakov

National Taras Shevchenko University of Kyiv

Abstract: Results on the convergence of sequences of solutions of non-linear equations and variational inequalities for obstacle problems are proved. The variational inequalities and equations are defined by a non-linear, pseudomonotone operator of the second order with periodic, rapidly oscillating coefficients and by sequences of functions characterizing the obstacles and the boundary conditions. Two-scale and macroscale (homogenized) limiting problems for such variational inequalities and equations are obtained. Results on the relationship between solutions of these limiting problems are established and sufficient conditions for the uniqueness of solutions are presented.
Bibliography: 25 titles.

DOI: https://doi.org/10.4213/sm1116

Full text: PDF file (699 kB)
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English version:
Sbornik: Mathematics, 2008, 199:1, 67–98

Bibliographic databases:

UDC: 517.956.8
MSC: 35B27
Received: 28.06.2005 and 14.09.2007

Citation: G. V. Sandrakov, “Homogenization of variational inequalities and equations defined by pseudomonotone operators”, Mat. Sb., 199:1 (2008), 67–100; Sb. Math., 199:1 (2008), 67–98

Citation in format AMSBIB
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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. Visintin A., “Scale-integration and scale-disintegration in nonlinear homogenization”, Calc. Var. Partial Differential Equations, 36:4 (2009), 565–590  crossref  mathscinet  zmath  isi  scopus
    2. Visintin A., “Homogenization of a parabolic model of ferromagnetism”, J. Differential Equations, 250:3 (2011), 1521–1552  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Gómez D., Lobo M., Pérez M.E., Shaposhnikova T.A., “Averaging in variational inequalities with nonlinear restrictions along manifolds”, Comptes Rendus Mécanique, 339:6 (2011), 406–410  crossref  adsnasa  isi  scopus
    4. Jäger W., Neuss-Radu M., Shaposhnikova T.A., “Scale limit of a variational inequality modeling diffusive flux in a domain with small holes and strong adsorption in case of a critical scaling”, Dokl. Math., 83:2 (2011), 204–208  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    5. Gómez D., Lobo M., Pérez M.E., Shaposhnikova T.A., “Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds”, Applicable Analysis, 92:2 (2013), 218–237  crossref  mathscinet  isi  scopus
    6. Visintin A., “Scale-Transformations and Homogenization of Maximal Monotone Relations with Applications”, Asymptotic Anal., 82:3-4 (2013), 233–270  crossref  mathscinet  zmath  isi  scopus
    7. Jäger W., Neuss-Radu M., Shaposhnikova T.A., “Homogenization of a variational inequality for the Laplace operator with nonlinear restriction for the flux on the interior boundary of a perforated domain”, Nonlinear Analysis: Real World Applications, 15 (2014), 367–380  crossref  mathscinet  zmath  isi  scopus
    8. Kovalevsky A.A., “On the convergence of solutions to bilateral problems with the zero lower constraint and an arbitrary upper constraint in variable domains”, Nonlinear Anal.-Theory Methods Appl., 147 (2016), 63–79  crossref  mathscinet  zmath  isi  scopus
    9. A. A. Kovalevskii, “Variatsionnye zadachi s odnostoronnimi potochechno funktsionalnymi ogranicheniyami v peremennykh oblastyakh”, Tr. IMM UrO RAN, 23, no. 2, 2017, 133–150  mathnet  crossref  elib
    10. A. A. Kovalevskii, “O skhodimosti reshenii variatsionnykh zadach s neyavnymi ogranicheniyami, zadannymi bystro ostsilliruyuschimi funktsiyami”, Tr. IMM UrO RAN, 24, no. 2, 2018, 107–122  mathnet  crossref  elib
    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 Sbornik: Mathematics (from 1967)
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