Mel’nyk, Taras A.; Klevtsovskiy, Arsen V. Asymptotic expansion for the solution of a convection-diffusion problem in a thin graph-like junction. (English) Zbl 1503.35177 Asymptotic Anal. 130, No. 3-4, 505-530 (2022). MSC: 35Q35 76R50 35C20 35B40 35R02 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{A. V. Klevtsovskiy}, Asymptotic Anal. 130, No. 3--4, 505--530 (2022; Zbl 1503.35177) Full Text: DOI arXiv
Mel’nyk, Taras Asymptotic approximations for eigenvalues and eigenfunctions of a spectral problem in a thin graph-like junction with a concentrated mass in the node. (English) Zbl 1476.35023 Anal. Appl., Singap. 19, No. 5, 875-939 (2021). MSC: 35B25 35B40 35C20 35J25 35P05 47A75 74K30 PDFBibTeX XMLCite \textit{T. Mel'nyk}, Anal. Appl., Singap. 19, No. 5, 875--939 (2021; Zbl 1476.35023) Full Text: DOI arXiv
Mel’nyk, Taras; Sadovyi, Dmytro Multiple-scale analysis of boundary-value problems in thick multi-level junctions of type \(3:2:2\). (English) Zbl 1443.35004 SpringerBriefs in Mathematics. Cham: Springer (ISBN 978-3-030-35536-4/pbk; 978-3-030-35537-1/ebook). viii, 105 p. (2019). Reviewer: Paolo Musolino (Padova) MSC: 35-02 35B27 35B40 PDFBibTeX XMLCite \textit{T. Mel'nyk} and \textit{D. Sadovyi}, Multiple-scale analysis of boundary-value problems in thick multi-level junctions of type \(3:2:2\). Cham: Springer (2019; Zbl 1443.35004) Full Text: DOI
Klevtsovskiy, A. V.; Mel’nyk, T. A. Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint. (English) Zbl 1348.35019 Asymptotic Anal. 97, No. 3-4, 265-290 (2016). Reviewer: Hussein Fakih (Nabatieh) MSC: 35B25 35C20 35J05 35B40 35J25 PDFBibTeX XMLCite \textit{A. V. Klevtsovskiy} and \textit{T. A. Mel'nyk}, Asymptotic Anal. 97, No. 3--4, 265--290 (2016; Zbl 1348.35019) Full Text: DOI arXiv
Mel’nyk, T. A.; Chechkin, G. A. Eigenvibrations of thick cascade junctions with ‘very heavy’ concentrated masses. (English) Zbl 1332.35028 Izv. Math. 79, No. 3, 467-511 (2015); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 79, No. 3, 41-86 (2015). Reviewer: Dan Polisevski (Bucureşti) MSC: 35B27 74K30 35P20 35B40 35J25 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{G. A. Chechkin}, Izv. Math. 79, No. 3, 467--511 (2015; Zbl 1332.35028); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 79, No. 3, 41--86 (2015) Full Text: DOI
Mel’nyk, Taras A. Asymptotic approximation for the solution to a semi-linear parabolic problem in a thick junction with the branched structure. (English) Zbl 1515.35037 J. Math. Anal. Appl. 424, No. 2, 1237-1260 (2015). MSC: 35B27 35C20 35K20 35K58 PDFBibTeX XMLCite \textit{T. A. Mel'nyk}, J. Math. Anal. Appl. 424, No. 2, 1237--1260 (2015; Zbl 1515.35037) Full Text: DOI arXiv
Mel’nik, T. A.; Popov, A. V. Asymptotic analysis of boundary value and spectral problems in thin perforated regions with rapidly changing thickness and different limiting dimensions. (English. Russian original) Zbl 1259.35025 Sb. Math. 203, No. 8, 1169-1195 (2012); translation from Mat. Sb. 203, No. 8, 97-124 (2012). Reviewer: Adrian Muntean (Eindhoven) MSC: 35B27 35P20 35J25 35C20 PDFBibTeX XMLCite \textit{T. A. Mel'nik} and \textit{A. V. Popov}, Sb. Math. 203, No. 8, 1169--1195 (2012; Zbl 1259.35025); translation from Mat. Sb. 203, No. 8, 97--124 (2012) Full Text: DOI
Chechkin, Gregory A.; Mel’nyk, Taras A. Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses. (English) Zbl 1254.35168 Appl. Anal. 91, No. 6, 1055-1095 (2012). Reviewer: Alain Brillard (Riedisheim) MSC: 35P20 35B27 35B40 47A75 74K30 PDFBibTeX XMLCite \textit{G. A. Chechkin} and \textit{T. A. Mel'nyk}, Appl. Anal. 91, No. 6, 1055--1095 (2012; Zbl 1254.35168) Full Text: DOI
Mel’nyk, Taras A.; Sivak, Olena A. Asymptotic approximations for solutions to quasilinear and linear elliptic problems with different perturbed boundary conditions in perforated domains. (English) Zbl 1233.35018 Asymptotic Anal. 75, No. 1-2, 79-92 (2011). Reviewer: Adrian Muntean (Eindhoven) MSC: 35B27 35J62 35B40 35J25 35R05 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{O. A. Sivak}, Asymptotic Anal. 75, No. 1--2, 79--92 (2011; Zbl 1233.35018) Full Text: Link
Mel’nyk, T. A.; Chechkin, G. A. Asymptotic analysis of boundary-value problems in thick cascade junctions. (Russian. English summary) Zbl 1164.35316 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 9, 16-22 (2008). MSC: 35B27 35B40 35C20 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{G. A. Chechkin}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 9, 16--22 (2008; Zbl 1164.35316)
Mel’nyk, Taras A. Homogenization of a boundary-value problem with a nonlinear boundary condition in a thick junction of type 3:2:1. (English) Zbl 1145.35327 Math. Methods Appl. Sci. 31, No. 9, 1005-1027 (2008). MSC: 35B27 35J65 35J60 74K30 PDFBibTeX XMLCite \textit{T. A. Mel'nyk}, Math. Methods Appl. Sci. 31, No. 9, 1005--1027 (2008; Zbl 1145.35327) Full Text: DOI
Mel’nik, T. A.; Vashchuk, P. S. Homogenization of a boundary value problem with mixed type of boundary conditions in a thick junction. (English. Russian original) Zbl 1140.35340 Differ. Equ. 43, No. 5, 696-703 (2007); translation from Differ. Uravn. 43, No. 5, 677-684 (2007). MSC: 35B27 35M10 35C20 PDFBibTeX XMLCite \textit{T. A. Mel'nik} and \textit{P. S. Vashchuk}, Differ. Equ. 43, No. 5, 696--703 (2007; Zbl 1140.35340); translation from Differ. Uravn. 43, No. 5, 677--684 (2007) Full Text: DOI
Durante, T.; Mel’nyk, T. A. Asymptotic analysis of a parabolic problem in a thick two-level junction. (English) Zbl 1144.35331 J. Math. Phys. Anal. Geom. 3, No. 3, 313-341 (2007). MSC: 35B27 74K30 35K20 35B40 35C20 74H10 PDFBibTeX XMLCite \textit{T. Durante} and \textit{T. A. Mel'nyk}, J. Math. Phys. Anal. Geom. 3, No. 3, 313--341 (2007; Zbl 1144.35331)
D’Apice, C.; De Maio, U.; Mel’nyk, T. A. Asymptotic analysis of a perturbed parabolic problem in a thick junction of type 3:2:2. (English) Zbl 1127.35310 Netw. Heterog. Media 2, No. 2, 255-277 (2007). MSC: 35B27 35B40 35C20 35K20 PDFBibTeX XMLCite \textit{C. D'Apice} et al., Netw. Heterog. Media 2, No. 2, 255--277 (2007; Zbl 1127.35310) Full Text: DOI
Mel’nyk, T. A.; Vashchuk, P. S. Homogenization of the Neumann-Fourier problem in a thick two-level junction of type 3:2:1. (English) Zbl 1141.35328 J. Math. Phys. Anal. Geom. 2, No. 3, 318-337 (2006). MSC: 35B27 35J25 35C20 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{P. S. Vashchuk}, J. Math. Phys. Anal. Geom. 2, No. 3, 318--337 (2006; Zbl 1141.35328)
De Maio, Umberto; Mel’nyk, Taras A. Asymptotic solution to a mixed boundary-value problem in a thick multi-structure of type 3:2:2. (English) Zbl 1211.35030 Ukr. Mat. Visn. 2, No. 4, 463-481 (2005) and in Ukr. Math. Bull. 2, No. 4, 467-485 (2005). MSC: 35B27 35J25 35C20 35B25 74K30 74Q05 PDFBibTeX XMLCite \textit{U. De Maio} and \textit{T. A. Mel'nyk}, Ukr. Mat. Visn. 2, No. 4, 463--481 (2005; Zbl 1211.35030)
De Maio, U.; Melnyk, Taras A.; Perugia, Carmen Homogenization of a Poisson boundary value problem in a plane thick two-level junction. (English) Zbl 1146.35007 Ric. Mat. 54, No. 2, 641-648 (2005). Reviewer: Yuri V. Rogovchenko (Kalmar) MSC: 35B27 35B40 35J25 35C20 35B25 PDFBibTeX XMLCite \textit{U. De Maio} et al., Ric. Mat. 54, No. 2, 641--648 (2005; Zbl 1146.35007)
De Maio, U.; Durante, Tiziana; Melnyk, Taras A. Asymptotic analysis of a mixed boundary value problem in a thick multi-level junction. (English) Zbl 1146.35006 Ric. Mat. 54, No. 2, 553-559 (2005). Reviewer: Yuri V. Rogovchenko (Kalmar) MSC: 35B27 35B40 35C20 74K30 PDFBibTeX XMLCite \textit{U. De Maio} et al., Ric. Mat. 54, No. 2, 553--559 (2005; Zbl 1146.35006)
De Maio, U.; Durante, T.; Mel’nyk, T. A. Asymptotic approximation for the solution to the Robin problem in a thick multi-level junction. (English) Zbl 1093.35011 Math. Models Methods Appl. Sci. 15, No. 12, 1897-1921 (2005). Reviewer: Marco Codegone (Torino) MSC: 35B27 35B40 35C20 74K30 PDFBibTeX XMLCite \textit{U. De Maio} et al., Math. Models Methods Appl. Sci. 15, No. 12, 1897--1921 (2005; Zbl 1093.35011) Full Text: DOI
De Maio, U.; Mel’nyk, T. A. Asymptotic analysis of the Neumann problem for the Ukawa equation in a thick multi-structure of type 3:2:2. (English) Zbl 1160.35327 Bandle, Catherine (ed.) et al., Elliptic and parabolic problems. A special tribute to the work of Haim Brezis. Basel: Birkhäuser (ISBN 3-7643-7249-4/hbk). Progress in Nonlinear Differential Equations and their Applications 63, 207-215 (2005). MSC: 35B25 35B27 35C20 35J25 PDFBibTeX XMLCite \textit{U. De Maio} and \textit{T. A. Mel'nyk}, Prog. Nonlinear Differ. Equ. Appl. 63, 207--215 (2005; Zbl 1160.35327) Full Text: DOI
De Maio, U.; Mel’nyk, T. A. Homogenization of the Neumann problem in thick multi-structures of type 3 : 2 : 2. (English) Zbl 1072.35029 Math. Methods Appl. Sci. 28, No. 7, 865-879 (2005). MSC: 35B27 35J25 35C20 35B25 PDFBibTeX XMLCite \textit{U. De Maio} and \textit{T. A. Mel'nyk}, Math. Methods Appl. Sci. 28, No. 7, 865--879 (2005; Zbl 1072.35029) Full Text: DOI
Mel’nyk, Taras A. Asymptotics of the spectrum of the Fourier problem in a thick junction of type 2:1:1. (Ukrainian. English summary) Zbl 0979.35111 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 1, 143-151 (2001). MSC: 35P20 35J25 35C20 74K10 PDFBibTeX XMLCite \textit{T. A. Mel'nyk}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 1, 143--151 (2001; Zbl 0979.35111)
Argatov, Ivan I.; Mel’nyk, Taras A. Homogenization of a contact problem for a system of densely situated punches. (English) Zbl 0996.74061 Eur. J. Mech., A, Solids 20, No. 1, 91-98 (2001). MSC: 74Q05 74M15 PDFBibTeX XMLCite \textit{I. I. Argatov} and \textit{T. A. Mel'nyk}, Eur. J. Mech., A, Solids 20, No. 1, 91--98 (2001; Zbl 0996.74061) Full Text: DOI
Mel’nyk, Taras Asymptotic behavior of eigenvalues and eigenfunctions of a boundary value problem in a thick periodic junction of type 3:2:2. (Ukrainian. English summary) Zbl 0985.35053 Visn. L’viv. Univ., Ser. Mekh.-Mat. 58, 153-159 (2000). MSC: 35P20 35J25 35C20 PDFBibTeX XMLCite \textit{T. Mel'nyk}, Visn. L'viv. Univ., Ser. Mekh.-Mat. 58, 153--159 (2000; Zbl 0985.35053)
Mel’nyk, T. A. Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1. (English) Zbl 0983.35044 Math. Methods Appl. Sci. 23, No. 4, 321-346 (2000). Reviewer: N.Weck (Essen) MSC: 35J25 35P20 35C20 35B25 PDFBibTeX XMLCite \textit{T. A. Mel'nyk}, Math. Methods Appl. Sci. 23, No. 4, 321--346 (2000; Zbl 0983.35044) Full Text: DOI
Mel’nik, T. A. Asymptotics of solutions of discontinuous singularly perturbed boundary value problems. (English. Russian original) Zbl 0940.34013 Ukr. Math. J. 51, No. 6, 963-967 (1999); translation from Ukr. Mat. Zh. 51, No. 6, 861-864 (1999). Reviewer: I.O.Parasyuk (Kyïv) MSC: 34B16 34B15 34E15 34E05 PDFBibTeX XMLCite \textit{T. A. Mel'nik}, Ukr. Mat. Zh. 51, No. 6, 861--864 (1999; Zbl 0940.34013); translation from Ukr. Mat. Zh. 51, No. 6, 861--864 (1999)
Mel’nik, T. A.; Nazarov, S. A. The asymptotics of the solution to the Neumann spectral problem in a domain of the “dense-comb” type. (English. Russian original) Zbl 0930.35114 J. Math. Sci., New York 85, No. 6, 2326-2346 (1997); translation from Tr. Semin. Im. I. G. Petrovskogo 19, 138-173 (1996). Reviewer: André Martinez (Bologna) MSC: 35P15 35B40 35R05 PDFBibTeX XMLCite \textit{T. A. Mel'nik} and \textit{S. A. Nazarov}, J. Math. Sci., New York 85, No. 6, 1 (1996; Zbl 0930.35114); translation from Tr. Semin. Im. I. G. Petrovskogo 19, 138--173 (1996)
Mel’nik, T. A. Asymptotic expansions of eigenvalues and eigenfunctions for elliptic boundary-value problems with rapidly oscillating coefficients in a perforated cube. (English. Russian original) Zbl 0844.35072 J. Math. Sci., New York 75, No. 3, 1646-1671 (1995); translation from Tr. Semin. Im. I. G. Petrovskogo 17, 51-88 (1994). MSC: 35P10 35B27 35J25 35C20 PDFBibTeX XMLCite \textit{T. A. Mel'nik}, J. Math. Sci., New York 75, No. 3, 1646--1671 (1994; Zbl 0844.35072); translation from Tr. Semin. Im. I. G. Petrovskogo 17, 51--88 (1994) Full Text: DOI
Mel’nik, T. A. Asymptotics of a solution to a discontinuous singularly perturbed Cauchy problem. (English. Russian original) Zbl 0946.34010 Ukr. Math. J. 46, No. 11, 1660-1666 (1994); translation from Ukr. Mat. Zh. 46, No. 11, 1502-1508 (1994). MSC: 34A36 34E15 34E05 PDFBibTeX XMLCite \textit{T. A. Mel'nik}, Ukr. Math. J. 46, No. 11, 1660--1666 (1994; Zbl 0946.34010); translation from Ukr. Mat. Zh. 46, No. 11, 1502--1508 (1994) Full Text: DOI
Mel’nik, T. A.; Nazarov, S. A. The asymptotic structure of the spectrum in the problem of harmonic oscillations of a hub with heavy spokes. (English. Russian original) Zbl 0827.35093 Russ. Acad. Sci., Dokl., Math. 48, No. 3, 428-432 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 333, No. 1, 13-15 (1993). MSC: 35P20 35C20 35J25 35B25 PDFBibTeX XMLCite \textit{T. A. Mel'nik} and \textit{S. A. Nazarov}, Russ. Acad. Sci., Dokl., Math. 48, No. 3, 1 (1993; Zbl 0827.35093); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 333, No. 1, 13--15 (1993)
Mel’nik, T. A. Spectral problems of the theory of averaging. (Russian) Zbl 0767.73044 Mathematics today, Sci.-Methodological Collect. 7, 86-115 (1992). MSC: 74E30 74K10 74-02 74E05 35B27 PDFBibTeX XMLCite \textit{T. A. Mel'nik}, in: Matematika segodnya. 1992. Nauchno-metodicheskij sbornik. Vyp. 7. Kiï|v: Vishcha Shkola. 86--115 (1992; Zbl 0767.73044)