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Uspekhi Mat. Nauk, 1981, Volume 36, Issue 1(217), Pages 11–58 (Mi umn2626)  

This article is cited in 36 scientific papers (total in 37 papers)

$G$-convergence of parabolic operators

V. V. Zhikov, S. M. Kozlov, O. A. Oleinik

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English version:
Russian Mathematical Surveys, 1981, 36:1, 9–60

Bibliographic databases:

UDC: 517.4+517.9
MSC: 35K90, 46B50, 47B07, 40A05, 47F05
Received: 30.09.1980

Citation: V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “$G$-convergence of parabolic operators”, Uspekhi Mat. Nauk, 36:1(217) (1981), 11–58; Russian Math. Surveys, 36:1 (1981), 9–60

Citation in format AMSBIB
\by V.~V.~Zhikov, S.~M.~Kozlov, O.~A.~Oleinik
\paper $G$-convergence of parabolic operators
\jour Uspekhi Mat. Nauk
\yr 1981
\vol 36
\issue 1(217)
\pages 11--58
\jour Russian Math. Surveys
\yr 1981
\vol 36
\issue 1
\pages 9--60

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    This publication is cited in the following articles:
    1. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “Averaging of parabolic operators with almost periodic coefficients”, Math. USSR-Sb., 45:1 (1983), 73–90  mathnet  crossref  mathscinet  zmath
    2. L. V. Berlyand, “The asymptotic behaviour of solutions of the first boundary-value problem of elasticity theory in domains with a finely-grained boundary”, Russian Math. Surveys, 38:6 (1983), 11–112  mathnet  crossref  mathscinet  zmath
    3. S. M. Kozlov, “A certain type of duality of functionals”, Funct. Anal. Appl., 17:3 (1983), 171–175  mathnet  crossref  mathscinet  isi
    4. F. O. Porper, S. D. Èidel'man, “Two-sided estimates of fundamental solutions of second-order parabolic equations, and some applications”, Russian Math. Surveys, 39:3 (1984), 119–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. M. Kozlov, “The method of averaging and walks in inhomogeneous environments”, Russian Math. Surveys, 40:12 (1985), 73–145  mathnet  crossref  mathscinet  zmath  adsnasa
    6. V. I. Arnol'd, M. I. Vishik, I. M. Gel'fand, Yu. V. Egorov, A. S. Kalashnikov, A. N. Kolmogorov, S. P. Novikov, S. L. Sobolev, “Ol'ga Arsen'evna Oleinik (on her sixtieth birthday)”, Russian Math. Surveys, 40:5 (1985), 267–287  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. S. M. Kozlov, “Averagind of difference schemes”, Math. USSR-Sb., 57:2 (1987), 351–369  mathnet  crossref  mathscinet  zmath
    8. V. V. Zhikov, “Averaging of functionals of the calculus of variations and elasticity theory”, Math. USSR-Izv., 29:1 (1987), 33–66  mathnet  crossref  mathscinet  zmath
    9. T. A. Shaposhnikova, “Averaging of the mixed problem for a parabolic equation in a perforated domain”, Russian Math. Surveys, 41:4 (1986), 185–186  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. José-Francisco Rodrigues, “The variational inequality approach to the”, Acta Appl Math, 8:1 (1987), 1  crossref  mathscinet  zmath  isi
    11. G. V. Sandrakov, “Averaging principles for eguations with rapidly oscillatory coefficients”, Math. USSR-Sb., 68:2 (1991), 503–553  mathnet  crossref  mathscinet  zmath  isi
    12. S. Gutman, “Identification of Discontinuous Parameters in Flow Equations”, SIAM J Control Optim, 28:5 (1990), 1049  crossref  mathscinet  zmath  isi
    13. V. L. Kamynin, “Limit passage in quasilinear parabolic equations with weakly converging coefficients, and the asymptotic behavior of solutions of the Cauchy problem”, Math. USSR-Sb., 70:2 (1991), 467–484  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. E. Ya. Khruslov, “An averaged model of a strongly inhomogeneous medium with memory”, Russian Math. Surveys, 45:1 (1990), 211–212  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. Nikolaos S. Papageorgiou, “Continuous dependence results for a class of evolution inclusions”, Proc Edin Math Soc, 35:1 (1992), 139  crossref  mathscinet  zmath  isi
    16. Nikolaos S Papageorgiou, “On the optimal control of strongly nonlinear evolution equations”, Journal of Mathematical Analysis and Applications, 164:1 (1992), 83  crossref
    17. Sergiu Aizicovici, Nikolaos S. Papageorgiou, “Infinite Dimensional Parametric Optimal Control Problems”, Math Nachr, 162:1 (1993), 17  crossref  mathscinet  zmath  isi
    18. Sergiu Aizicovici, Nikolaos S. Papageorgiou, “Infinite dimensional parametric optimal control problems”, Japan J Indust Appl Math, 10:2 (1993), 307  crossref  mathscinet  zmath
    19. V. L. Kamynin, “An approach to the mathematical modelling of highly heterogeneous flows of a viscous incompressible fluid”, Comput. Math. Math. Phys., 33:5 (1993), 649–661  mathnet  mathscinet  zmath  isi
    20. NIKOLAOS S. PAPAGEORGIOU, “Optimization of controlled evolution equations under indeterminacy conditions”, International Journal of Systems Science, 24:12 (1993), 2303  crossref
    21. A. A. Kovalevsky, “$G$-convergence and homogenization of nonlinear elliptic operators in divergence form with variable domain”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 431–460  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. Shouchuan Hu, V. Lakshmikantham, Nikolaos S. Papageorgiou, “On the properties of the solution set of semilinear evolution inclusions”, Nonlinear Analysis: Theory, Methods & Applications, 24:12 (1995), 1683  crossref
    23. Andrea Dall'Aglio, “Approximated solutions of equations withL 1 data. Application to theH-convergence of quasi-linear parabolic equations”, Annali di Matematica, 170:1 (1996), 207  crossref  mathscinet  zmath  isi
    24. Nikolaos S. Papageorgiou, “On the variational stability of a class of nonlinear parabolic optimal control problems”, J Aust Math Soc Series B Appl Math, 39:1 (1997), 77  crossref  mathscinet  zmath  isi
    25. Nikolaos S. Papageorgiou, “On the Existence of Solutions for Nonlinear Parabolic Problems with Nonmonotone Discontinuities”, Journal of Mathematical Analysis and Applications, 205:2 (1997), 434  crossref
    26. Dimitrios A. Kandilakis, Nikolaos S. Papageorgiou, “Nonlinear periodic parabolic problems with nonmonotone discontinuities”, Proc Edin Math Soc, 41:1 (1998), 117  crossref  mathscinet  zmath  isi
    27. F. Paronetto, F. Serra Cassano, “On the convergence of a class of degenerate parabolic equations”, Journal de Mathématiques Pures et Appliquées, 77:9 (1998), 851  crossref
    28. Nikolaos S. Papageorgiou, Nikolaos Yannakakis, “Minimax Control of Nonlinear Evolution Equations”, Journal of Mathematical Analysis and Applications, 259:2 (2001), 509  crossref
    29. Sijue Wu, “Homogenization of Differential Operators”, Acta Math Appl Sin Engl Ser, 18:1 (2002), 9  crossref  mathscinet  zmath  elib
    30. Nikolaos S. Papageorgiou, Nikolaos Yannakakis, “Minimax control of nonlinear evolution equations”, Applied Mathematics and Computation, 131:2-3 (2002), 271  crossref
    31. V. B. Levenshtam, “Unique Solvability of Parabolic Equations with Almost-Periodic Coefficients in Hölder Spaces”, Math. Notes, 73:6 (2003), 813–828  mathnet  crossref  crossref  mathscinet  zmath  isi
    32. A. A. Tolstonogov, “On solutions of an evolution control system depending on parameters”, Sb. Math., 194:9 (2003), 1383–1409  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    33. Pierre Étoré, Antoine Lejay, “A Donsker theorem to simulate one-dimensional processes with measurable coefficients”, Probability and Statistics, 11 (2007), 301  crossref  mathscinet  zmath
    34. Fabio Paronetto, “G-convergence of mixed type evolution operators”, Journal de Mathématiques Pures et Appliquées, 93:4 (2010), 361  crossref
    35. V. S. Klimov, “The Bohl index of a homogeneous parabolic inclusion”, Izv. Math., 75:2 (2011), 347–370  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    36. Krešimir Burazin, Marko Vrdoljak, “Homogenisation theory for Friedrichs systems”, CPAA, 13:3 (2013), 1017  crossref
    37. A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem”, Journal of Mathematical Sciences, 216:3 (2016), 345–496  mathnet  crossref
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