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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 2(10), Pages 187–217 (Mi msb2457)  

This article is cited in 26 scientific papers (total in 26 papers)

Asymptotics of solutions of the Dirichlet problem in a domain with a truncated thin tube

V. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii


Abstract: Asymptotic expansions (as $\varepsilon\to0$) of solutions of the Dirichlet problem are obtained for a strongly elliptic equation of order $2m$ in a subdomain of $\mathbf R^n$ minus an $\varepsilon$-neighborhood of a smooth submanifold, without boundary, of positive codimension.
Bibliography: 18 titles.

Full text: PDF file (2413 kB)
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English version:
Mathematics of the USSR-Sbornik, 1983, 44:2, 167–194

Bibliographic databases:

UDC: 517.96
MSC: 35J40, 35B40
Received: 16.06.1980

Citation: V. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii, “Asymptotics of solutions of the Dirichlet problem in a domain with a truncated thin tube”, Mat. Sb. (N.S.), 116(158):2(10) (1981), 187–217; Math. USSR-Sb., 44:2 (1983), 167–194

Citation in format AMSBIB
\Bibitem{MazNazPla81}
\by V.~G.~Maz'ya, S.~A.~Nazarov, B.~A.~Plamenevskii
\paper Asymptotics of solutions of the Dirichlet problem in a~domain with a~truncated thin tube
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 2(10)
\pages 187--217
\mathnet{http://mi.mathnet.ru/msb2457}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=637860}
\zmath{https://zbmath.org/?q=an:0502.35017|0473.35019}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 2
\pages 167--194
\crossref{https://doi.org/10.1070/SM1983v044n02ABEH000959}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kiselev A., “Thin Cylindrical Emitter in Inhomogeneous Elastic Medium”, Zhurnal Tek. Fiz., 54:2 (1984), 209–215  mathscinet  isi
    2. M. V. Fedoryuk, “Scattering of a plane wave by a cylindrical surface with a long perturbation”, Math. USSR-Izv., 26:1 (1986), 153–184  mathnet  crossref  mathscinet  zmath
    3. Krutin V. Fedoriuk M., “Mixed Short-Long-Wavelength Approximations in the Dynamics of Viscoelastic Media”, 280, no. 6, 1985, 1334–1337  mathscinet  zmath  isi
    4. I. Yu. Popov, “Extension theory and localization of resonances for domains of trap type”, Math. USSR-Sb., 71:1 (1992), 209–234  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. A. Nazarov, “Asymptotic solution of a variational inequality modelling a friction”, Math. USSR-Izv., 37:2 (1991), 337–369  mathnet  crossref  mathscinet  zmath  adsnasa
    6. Popov I., “Substantiation of the Model of Zero Width Slits for the Neumann Problem”, 313, no. 4, 1990, 806–811  mathscinet  zmath  isi
    7. I. Yu. Popov, “The Helmholtz resonator and the theory of operator extensions in a space with indefinite metric”, Russian Acad. Sci. Sb. Math., 75:2 (1993), 285–315  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. Argatov I., Nazarov S., “Junction Problem of Shashlik (Skewer) Type”, Comptes Rendus Acad. Sci. Ser. I-Math., 316:12 (1993), 1329–1334  mathscinet  zmath  isi
    9. I. I. Argatov, S. A. Nazarov, “Asymptotic solution of the Signorini problem with an obstacle on a thin elongated set”, Sb. Math., 187:10 (1996), 1411–1442  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. I. I. Argatov, S. A. Nazarov, “Asymptotic analysis of problems on junctions of domains of different limit dimensions. A body pierced by a thin rod”, Izv. Math., 60:1 (1996), 1–37  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Argatov I., Nazarov S., “The Pressure of a Narrow Ring-Shaped Punch on an Elastic Half-Space”, Pmm-J. Appl. Math. Mech., 60:5 (1996), 799–812  crossref  mathscinet  zmath  isi
    12. R. R. Gadyl'shin, “Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator”, Russian Math. Surveys, 52:1 (1997), 1–72  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. Argatov I., “Pressure of a Narrow Band-Like Punch Upon an Elastic Half-Space”, Int. Appl. Mech., 36:10 (2000), 1363–1368  crossref  zmath  isi
    14. Argatov I., “The Method of Averaging in a Contact Problem for a System of Punches”, Pmm-J. Appl. Math. Mech., 68:1 (2004), 93–104  crossref  mathscinet  zmath  isi
    15. I. I. Argatov, “Asymptotics of the reduced logarithmic capacity of a narrow cylinder”, Math. Notes, 77:1 (2005), 15–25  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. I. I. Argatov, “Asymptotics of a reduced logarithmic capacity”, Comput. Math. Math. Phys., 45:1 (2005), 120–137  mathnet  mathscinet  zmath  elib  elib
    17. Ivan I. Argatov, Federico J. Sabina, “Acoustic diffraction by a thin soft torus”, Wave Motion, 45:6 (2008), 846  crossref
    18. M A Lyalinov, S V Polyanskaya, “Scattering and radiation of waves by a thin toroidal tube with semi-transparent walls: an asymptotic model”, J. Phys. A: Math. Theor, 44:33 (2011), 335206  crossref
    19. Ivan Argatov, Igor Sevostianov, “Rigid toroidal inhomogeneity in an elastic medium”, International Journal of Engineering Science, 49:1 (2011), 61  crossref
    20. Postnikova E.Yu., “Asimptotika kraevoi zadachi v oblasti s dvumya otverstiyami”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 26, 49–58  elib
    21. E. Yu. Postnikova, “Asimptotika kraevoi zadachi v oblasti s dvumya otverstiyami”, Vestnik ChelGU, 2011, no. 13, 49–58  mathnet
    22. V. A. Kozlov, S. A. Nazarov, “Asymptotic model of interaction of blood flow with vein walls and the surrounding muscular tissue”, Dokl. Phys, 57:10 (2012), 411  crossref
    23. V. A. Kozlov, S. A. Nazarov, “Asymptotic models of the blood flow in arterias and veins”, J. Math. Sci. (N. Y.), 194:1 (2013), 44–57  mathnet  crossref  mathscinet
    24. Kozlov V.A., Nazarov S.A., “Asimptoticheskaya model vzaimodeistviya potoka krovi so stenkami veny i okruzhayuschei myshechnoi tkanyu”, Doklady akademii nauk, 446:6 (2012), 631–631  elib
    25. S. A. Nazarov, “Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle”, Izv. Math., 77:1 (2013), 87–142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    26. S. A. Nazarov, “Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube”, Trans. Moscow Math. Soc., 76:1 (2015), 1–53  mathnet  crossref  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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