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

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
\Bibitem{Pan79} \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 \mathnet{http://mi.mathnet.ru/msb2508} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=562207} \zmath{https://zbmath.org/?q=an:0462.35007|0442.35009} \transl \jour Math. USSR-Sb. \yr 1981 \vol 38 \issue 4 \pages 465--494 \crossref{https://doi.org/10.1070/SM1981v038n04ABEH001453} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LQ11400003} 

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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
2. Kosarev A., “Asymptotic-Behavior of Effective Coefficients of Elastic Periodic Media with Highly Varying Properties”, 267, no. 1, 1982, 38–42
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
4. A. L. Piatnitski, “Averaging a singularly perturbed equation with rapidly oscillating coefficients in a layer”, Math. USSR-Sb., 49:1 (1984), 19–40
5. G. P. Panasenko, “Averaging processes in framework structures”, Math. USSR-Sb., 50:1 (1985), 213–225
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
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
8. S. M. Kozlov, A. L. Piatnitski, “Averaging on a background of vanishing viscosity”, Math. USSR-Sb., 70:1 (1991), 241–261
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
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
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
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
13. Panasenko G., “Asymptotic Analysis of Bar Systems .2.”, Russ. J. Math. Phys., 4:1 (1996), 87–116
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
15. Panasenko G., “Method of Asymptotic Partial Decomposition of Domain”, Math. Models Meth. Appl. Sci., 8:1 (1998), 139–156
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
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
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
19. Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S161–S167
20. Panasenko G., “The Partial Homogenization: Continuous and Semi-Discretized Versions”, Math. Models Meth. Appl. Sci., 17:8 (2007), 1183–1209
21. A.G. Kolpakov, “Influence of non degenerated joint on the global and local behavior of joined plates”, International Journal of Engineering Science, 2011
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
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
24. S. A. Nazarov, “Osrednenie plastin Kirkhgofa, soedinennykh zaklepkami, kotorye modeliruyutsya tochechnymi usloviyami Soboleva”, Algebra i analiz, 32:2 (2020), 143–200
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