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Mat. Sb. (N.S.), 1979, Volume 110(152), Number 4(12), Pages 505–538 (Mi msb2508)  

This article is cited in 24 scientific papers (total in 24 papers)

Higher order asymptotics of solutions of problems on the contact of periodic structures

G. P. Panasenko


Abstract: A methodology is proposed for averaging in boundary value problems with plane bondary, and also problems on the contact of several microstructures with plane contact surface. Boundary layers are taken into account in this methodology. The author considers both direct contact of two structures and contact of two media separated by a thin inhomogeneous layer having periodic structure. Formal asymptotic solutions of some problems on the contact of two media are constructed, and estimates of how close the asymptotic solution is to the exact solution are derived.
Bibliography: 34 titles.

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English version:
Mathematics of the USSR-Sbornik, 1981, 38:4, 465–494

Bibliographic databases:

UDC: 517.946.9
MSC: 35B40

Citation: G. P. Panasenko, “Higher order asymptotics of solutions of problems on the contact of periodic structures”, Mat. Sb. (N.S.), 110(152):4(12) (1979), 505–538; Math. USSR-Sb., 38:4 (1981), 465–494

Citation in format AMSBIB
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\by G.~P.~Panasenko
\paper Higher order asymptotics of solutions of problems on the contact of periodic structures
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 110(152)
\issue 4(12)
\pages 505--538
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\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 4
\pages 465--494
\crossref{https://doi.org/10.1070/SM1981v038n04ABEH001453}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “$G$-convergence of parabolic operators”, Russian Math. Surveys, 36:1 (1981), 9–60  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Kosarev A., “Asymptotic-Behavior of Effective Coefficients of Elastic Periodic Media with Highly Varying Properties”, 267, no. 1, 1982, 38–42  mathscinet  zmath  isi
    3. Iosifian G., Oleinik O., Panasenko G., “Asymptotic-Expansion of Solution for a System of the Elasticity Theory Equations with Periodic, Fast Oscillating Coefficients”, 266, no. 1, 1982, 18–22  mathscinet  isi
    4. A. L. Piatnitski, “Averaging a singularly perturbed equation with rapidly oscillating coefficients in a layer”, Math. USSR-Sb., 49:1 (1984), 19–40  mathnet  crossref  mathscinet  zmath
    5. G. P. Panasenko, “Averaging processes in framework structures”, Math. USSR-Sb., 50:1 (1985), 213–225  mathnet  crossref  mathscinet  zmath
    6. Oleinik O. Panasenko G. Yosifian G., “Homogenization and Asymptotic Expansions for Solutions of the Elasticity System with Rapidly Oscillating Periodic Coefficients”, 15, no. 1-4, 1983, 15–32  mathscinet  zmath  isi
    7. Nazarov S., “The Constants in the Asymptotics of Solutions of Eliptic Boundary-Value Problems with Periodic Coefficients in a Cylinder”, no. 3, 1985, 16–22  mathscinet  zmath  isi
    8. S. M. Kozlov, A. L. Piatnitski, “Averaging on a background of vanishing viscosity”, Math. USSR-Sb., 70:1 (1991), 241–261  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. S. A. Nazarov, “Asymptotics of the solution of the Dirichlet problem for an equation with rapidly oscillating coefficients in a rectangle”, Math. USSR-Sb., 73:1 (1992), 79–110  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. M. V. Kozlova, G. P. Panasenko, “Averaging of a three-dimensional problem of elasticity theory for an inhomogeneous rod”, U.S.S.R. Comput. Math. Math. Phys., 31:10 (1991), 128–131  mathnet  mathscinet  zmath  isi
    11. Taimurazova L., “Boundary-Layer Method for Boundary-Problem with Rapidly Oscillating and Strongly Varying Coefficients”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1991, no. 6, 79–83  mathscinet  isi
    12. Gnelecoumbaga S., Panasenko G., “On the Problem of Contact of Highly Conductive and Perforated Domains”, Comptes Rendus Acad. Sci. Ser. I-Math., 321:6 (1995), 809–815  mathscinet  zmath  isi
    13. Panasenko G., “Asymptotic Analysis of Bar Systems .2.”, Russ. J. Math. Phys., 4:1 (1996), 87–116  mathscinet  zmath  isi
    14. S. A. Nazarov, A. S. Slutskij, “Asymptotic behaviour of solutions of boundary-value problems for equations with rapidly oscillating coefficients in a domain with a small cavity”, Sb. Math., 189:9 (1998), 1385–1422  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. Panasenko G., “Method of Asymptotic Partial Decomposition of Domain”, Math. Models Meth. Appl. Sci., 8:1 (1998), 139–156  crossref  mathscinet  zmath  isi
    16. S. Gnélécoumbaga, G. P. Panasenko, “Asymptotic analysis of the problem of contact of a highly conducting and a perforated domain”, Comput. Math. Math. Phys., 39:1 (1999), 65–80  mathnet  mathscinet  zmath
    17. Teplinskii A., “Asymptotic Expansions for the Eigenvalues and the Eigenfunctions of Boundary Value Problems with Rapidly Oscillating Coefficients in a Layer”, Differ. Equ., 36:6 (2000), 911–917  mathnet  crossref  mathscinet  isi
    18. Demidov A., “Some Applications of the Helmholtz-Kirchhoff Method (Equilibrium Plasma in Tokamaks, Hele-Shaw Flow, and High-Frequency Asymptotics”, Russ. J. Math. Phys., 7:2 (2000), 166–186  mathscinet  zmath  isi
    19. Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S161–S167  mathnet  mathscinet  zmath  elib
    20. Panasenko G., “The Partial Homogenization: Continuous and Semi-Discretized Versions”, Math. Models Meth. Appl. Sci., 17:8 (2007), 1183–1209  crossref  mathscinet  zmath  isi
    21. A.G. Kolpakov, “Influence of non degenerated joint on the global and local behavior of joined plates”, International Journal of Engineering Science, 2011  crossref
    22. Holloway Ch.L., Kuester E.F., “Corrections to the Classical Continuity Boundary Conditions at the Interface of a Composite Medium”, Photonics Nanostruct., 11:4 (2013), 397–422  crossref  mathscinet  isi
    23. Kolpakov A.G., Andrianov I.V., Rakin S.I., Rogerson G.A., “An Asymptotic Strategy to Couple Homogenized Elastic Structures”, Int. J. Eng. Sci., 131 (2018), 26–39  crossref  mathscinet  zmath  isi  scopus
    24. S. A. Nazarov, “Osrednenie plastin Kirkhgofa, soedinennykh zaklepkami, kotorye modeliruyutsya tochechnymi usloviyami Soboleva”, Algebra i analiz, 32:2 (2020), 143–200  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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