| Reference |
1. D. Blanchard, A. Gaudiello, T.A. Mel’nyk, Boundary Homogenization and Reduction of Dimension in
a Kirchhoff-Love Plate, SIAM Journal on Mathematical Analysis, 39 (2008), ¹6, 1764–1787.
2. D. Blanchard, A. Gaudiello, J. Mossino, Highly Oscillating Boundaries and Reduction of Dimension: the
Critical Case, Analysis and Application, 5 (2007), 137–163.
3. D. Blanchard, A. Gaudiello, G. Griso, Junction of a Periodic Family of Elastic Rods with 3d Plate, J.
Math. Pures Appl., 88 (2007), ¹9, 1–33 (Part I); J. Math. Pures Appl., 88 (2007), ¹9, 149–190 (Part
II).
4. G.A. Chechkin, T.A. Mel’nyk, Asymptotics of Eigenelements to Spectral Problem in Thick Cascade
Junction with Concentrated Masses, Applicable Analysis; http:// www.tandfonline.com/doi/abs/DOI:
10.1080/00036811.2011.602634.
5. C. D’Apice, U. De Maio, T.A. Mel’nyk, Asymptotic Analysis of a Perturbed Parabolic Problem in a
Thick Junction of Type 3:2:2, Networks and Heterogeneous Media, 2 (2007), .2, 255–277.
6. U. De Maio, T.A. Mel’nyk, Asymptotic Solution to a Mixed Boundary-Value Problem in a Thick Multi-
Structure of Type 3:2:2, Ukrainian Mathematical Bulletin, 2 (2005), ¹4, 467–485.
7. U. De Maio, T. Durante, T.A. Mel’nyk, Asymptotic Approximation for the Solution to the Robin
Problem in a Thick Multi-Level Junction, Mathematical Models and Methods in Applied Sciences,
(M3AS), 15 (2005), ¹12, 1897–1921.
8. T. Durante, T.A. Mel’nyk, Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction,
Journal of Math. Physics, Analysis, Geometry, 3 (2007), ¹3, 313–341.
9. H. Gaevsky, K. Greger, K. Zakharias, Nonlinear Operator Equations and Operator Differential Equations,
Mir, Moscow, 1975. (in Russian)
10. E.Ya. Khruslov, On the Resonance Phenomenas in One Problem of Diffraction, Teor. Funkts., Funkts.
Anal. i Prilozhen, 10 (1968), 113–120. (in Russian)
11. V.P. Kotliarov, E.Ya. Khruslov, On a Limit Boundary Condition of Some Neumann Problem, Teor.
Funkts., Funkts. Anal. i Prilozhen, 10 (1970), 83–96. (in Russian)
12. Y.I. Lavrentovich, T.V. Knyzkova, V.V. Pidlisnyuk, The Potential of Application of New Nanostructural
Materials for Degradation of Pesticides in Water, Proceedings of the 7th International HCH and Pesticides
Forum “Towards the establishment of an obsolete POPS/pecticides stockpile fund for Central and
Eastern European countries and new independent states” (Kyiv, June 5–7, 2003), (2003), 167–169.
13. M. Lenczner, Multiscale Model for Atomic Force Microscope Array Mechanical Behavior, Applied
Physics Letters, 90 (2007), 901–908.
14. S.E. Lyshevshi, Mems and Nems: Systems, Devices, and Structures, CRC Press, Boca Raton, FL, 2002.
15. V.A. Marchenko, E.Ya. Khruslov, Boundary Value Problems in Domains with Finegrained Boundary,
Naukova Dumka, Kiev, 1974. (in Russian)
16. T.A. Mel’nik, P.S. Vashchuk, Homogenization of a Boundary-Value Problem with Mixed Type of
Boundary Conditions in a Thick Junction, Partial Differential Equations, 43 (2007), ¹5, 677–684.
17. T.A. Mel’nyk, S.A. Nazarov, The Asymptotic Structure of the Spectrum in the Problem of Harmonic
Oscillations of a Hub with Heavy Spokes, Russ. Acad. Sci. Dokl. Math., 48 (1994), ¹3, 428–432.
18. T.A. Mel’nyk, S.A. Nazarov, Asymptotics of the Neumann Spectral Problem Solution in a Domain of
“Thick Comb”, Tr. Sem. im. I.G. Petrovskogo, 19 (1996), 138–174. (in Russian)
19. T.A. Mel’nyk, Homogenization of the Poisson Equation in a Thick Periodic Junction, Zeitschrift f.ur
Analysis und ihre Anwendungen, 18 (1999), ¹4, 953–975.
20. T.A. Mel’nyk, S.A. Nazarov, Asymptotic Analysis of the Neumann Problem of the Junction of a Body
and Thin Heavy Rods, St.-Petersburg Math. J., 12 (2001), ¹2, 317–351.
21. T.A. Mel’nyk, Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction
of the Type 3:2:1, Ukr. Math. J., 52 (2000), ¹11, 1737–1748.
22. T.A. Mel’nyk, Homogenization of a Boundary-Value Problem with a Nonlinear Boundary Condition in
a Thick Junction of Type 3:2:1, Math. Models Meth. Appl. Sci., 31 (2008), 1005–1027.
23. T.A. Mel’nyk, G.A. Chechkin, Homogenization of a Boundary-Value Problem in a Thick 3-dimensional
Multi-Level Junction, Russian Academy of Sciences. Sbornik. Mathematics, 200 (2009), ¹3, 357–383.
24. T.A. Mel’nyk, D.Yu. Sadovyj, Homogenization of Quasilinear Parabolic Problem with Various Alternating
Nonlinear Fourier Boundary Conditions in a Two-Level Thick Junction of Type 3:2:2, Ukr. Math.
J., 63 (2012), ¹12.
25. T.A. Mel’nyk, D.Yu. Sadovyj, Homogenization of Quasilinear Parabolic Problems with alternating nonlinear
Fourier and Uniform Dirichlet Boundary Conditions in a Thick Two-Level Junction of Type 3:2:2,
Mat. Visnyk NTSh, 7 (2011), 115–136. (in Ukrainian)
26. T.A. Mel’nyk, O.A. Sivak, Asymptotic Analysis of a Parabolic Semilinear Problem with Nonlinear
Boundary Multiphase Interactions in a Perforated Domain, J. Math. Sci., 164 (2010), ¹3, 427–454.
27. S.A. Nazarov, Junctions of Singularly Degenerating Domains with Different Limit Dimension, Tr. Sem.
im. I. G. Petrovskogo, 18 (1995), 1–78 (Part I); Tr. Sem. im. I. G. Petrovskogo, 20 (2000), 155–196
(Part II). (in Russian)
28. S.A. Nazarov, The Polynomial Property Selfadjoint Elliptic Boundary-Value Problems and Algebraic
Description Their Atributes, Usp. Mat. Nauk, 54 (1999), ¹5, 77–142. (in Russian)
29. S.A. Nazarov, B.A. Plamenevskii, Elliptic Problems in Domains with Piecewise Smooth Boundaries,
Walter de Gruyter, Berlin, 1994
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