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Mat. Sb., 2009, Volume 200, Number 3, Pages 49–74 (Mi msb4500)  

This article is cited in 12 scientific papers (total in 12 papers)

Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions

T. A. Mel'nika, G. A. Chechkinbc

a National Taras Shevchenko University of Kyiv, The Faculty of Mechanics and Mathematics
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c Narvik University College

Abstract: We consider homogenization problems in a singularly perturbed three-dimensional domain of multi-level-junction type which consists of the junction body and a large number of alternating thin curvilinear cylinders that belong to two classes. Under the assumption that one class consists of cylinders of finite height, and the second class of cylinders of infinitesimal height, and that different inhomogeneous boundary conditions of the third kind with perturbed coefficients are given on the boundaries of the thin curvilinear cylinders, we prove the homogenization theorems and the convergence of the energy integrals.
Bibliography: 42 titles.

Keywords: homogenization, thick junctions, asymptotics.
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English version:
Sbornik: Mathematics, 2009, 200:3, 357–383

Bibliographic databases:

UDC: 517.956.225+517.956.8
MSC: Primary 35B40; Secondary 35B25, 35B27, 35J25
Received: 18.12.2007 and 02.07.2008

Citation: T. A. Mel'nik, G. A. Chechkin, “Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions”, Mat. Sb., 200:3 (2009), 49–74; Sb. Math., 200:3 (2009), 357–383

Citation in format AMSBIB
\by T.~A.~Mel'nik, G.~A.~Chechkin
\paper Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions
\jour Mat. Sb.
\yr 2009
\vol 200
\issue 3
\pages 49--74
\jour Sb. Math.
\yr 2009
\vol 200
\issue 3
\pages 357--383

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    This publication is cited in the following articles:
    1. Chechkin G.A., Chechkina T.P., D'Apice C., De Maio U., Mel'nyk T.A., “Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction”, Russ. J. Math. Phys., 17:1 (2010), 35–55  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. T. P. Chechkina, “Convergence of solutions of a boundary-value problem in a thick cascade junction with oscillating boundary of the transmission zone in the case of Neumann conditions at the boundary”, Russian Math. Surveys, 65:5 (2010), 982–983  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. G. A. Chechkin, C. D'Apice, U. De Maio, “On the rate of convergence of solutions in domain with periodic multilevel oscillating boundary”, Math. Meth. Appl. Sci., 33:17 (2010), 2019–2036  crossref  mathscinet  zmath  elib  scopus  scopus
    4. T. P. Chechkina, “Averaging in cascade junctions with a “wide” transmission domain”, Journal of Mathematical Sciences, 190:1 (2013), 157–169  mathnet  crossref  mathscinet
    5. Chechkin G.A., Mel'nyk T.A., “Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses”, Appl. Anal., 91:6 (2012), 1055–1095  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Mel'nyk T.A., Sadovyi D.Yu., “Homogenization of a quasilinear parabolic problem with different alternating nonlinear Fourier boundary conditions in a two-level thick junction of the type 3:2:2”, Ukr. Math. J., 63:12 (2012), 1855–1882  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Durante T., Mel'nyk T.A., “Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3:2:1”, ESAIM Control Optim. Calc. Var., 18:2 (2012), 583–610  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Mel'nik T.A., Chechkin G.A., “On new types of vibrations of thick cascade junctions with concentrated masses”, Dokl. Math., 87:1 (2013), 102  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    9. G. A. Chechkin, T. A. Mel'nyk, “Spatial-skin effect for eigenvibrations of a thick cascade junction with ‘heavy’ concentrated masses”, Math. Methods Appl. Sci., 37:1 (2014), 56–74  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. G. A. Chechkin, C. D'Apice, U. De Maio, A. L. Piatnitski, “On the rate of convergence of solutions in domain with random multilevel oscillating boundary”, Asymptot. Anal., 87:1-2 (2014), 1–28  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Zhao J., Wang J., “Convergence Rates in Homogenization of the Mixed Boundary Value Problems”, Math. Probl. Eng., 2019, 2680657  crossref  mathscinet  isi  scopus
    12. Zhao J., Wang J., “Homogenization of Nonlinear Equations With Mixed Boundary Conditions”, J. Math. Phys., 60:8 (2019), 081512  crossref  mathscinet  zmath  isi
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