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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.
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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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\paper Higher order asymptotics of solutions of problems on the contact of periodic structures
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\yr 1979
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\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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This publication is cited in the following articles:
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V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “$G$-convergence of parabolic operators”, Russian Math. Surveys, 36:1 (1981), 9–60
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Kosarev A., “Asymptotic-Behavior of Effective Coefficients of Elastic Periodic Media with Highly Varying Properties”, 267, no. 1, 1982, 38–42
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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
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A. L. Piatnitski, “Averaging a singularly perturbed equation with rapidly oscillating coefficients in a layer”, Math. USSR-Sb., 49:1 (1984), 19–40
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G. P. Panasenko, “Averaging processes in framework structures”, Math. USSR-Sb., 50:1 (1985), 213–225
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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
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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
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S. M. Kozlov, A. L. Piatnitski, “Averaging on a background of vanishing viscosity”, Math. USSR-Sb., 70:1 (1991), 241–261
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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
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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
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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
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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
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Panasenko G., “Asymptotic Analysis of Bar Systems .2.”, Russ. J. Math. Phys., 4:1 (1996), 87–116
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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
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Panasenko G., “Method of Asymptotic Partial Decomposition of Domain”, Math. Models Meth. Appl. Sci., 8:1 (1998), 139–156
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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
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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
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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
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Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S161–S167
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Panasenko G., “The Partial Homogenization: Continuous and Semi-Discretized Versions”, Math. Models Meth. Appl. Sci., 17:8 (2007), 1183–1209
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A.G. Kolpakov, “Influence of non degenerated joint on the global and local behavior of joined plates”, International Journal of Engineering Science, 2011
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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
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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
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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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