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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 1, Pages 167–186 (Mi izv1552)  

This article is cited in 25 scientific papers (total in 25 papers)

Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a slender cylinder

M. V. Fedoryuk


Abstract: The Dirichlet problem is investigated for the Laplace and Helmholtz equations in the exterior of a surface in $\mathbf R^3$ which is a right circular cylinder outside a sphere. Asymptotic expansions of the solutions are constructed; the small parameter is the maximal diameter of the cross-section of the cylinder.
Bibliography: 8 titles.

Full text: PDF file (1490 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:1, 145–161

Bibliographic databases:

UDC: 517.9
MSC: 35J05, 35B40
Received: 12.03.1980

Citation: M. V. Fedoryuk, “Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a slender cylinder”, Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981), 167–186; Math. USSR-Izv., 18:1 (1982), 145–161

Citation in format AMSBIB
\Bibitem{Fed81}
\by M.~V.~Fedoryuk
\paper Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a~slender cylinder
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 1
\pages 167--186
\mathnet{http://mi.mathnet.ru/izv1552}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=607581}
\zmath{https://zbmath.org/?q=an:0483.35021|0477.35034}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 1
\pages 145--161
\crossref{https://doi.org/10.1070/IM1982v018n01ABEH001377}


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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. V. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii, “Asymptotics of the solution of the Dirichlet problem in domains with a thin crosspiece”, Funct. Anal. Appl., 16:2 (1982), 108–114  mathnet  crossref  mathscinet  zmath  isi
    2. G. V. Zhdanova, “Scattering of plane longitudinal elastic waves by a slender cavity of revolution. The case of axial incidence”, Math. USSR-Sb., 49:2 (1984), 305–323  mathnet  crossref  mathscinet  zmath
    3. Zorin I., Nazarov S., “Strain-Stress State Asymptotics of Elastic Space with a Rigid Toroidal Inclusion”, 272, no. 6, 1983, 1340–1343  zmath  isi
    4. Zhdanova G., “Dispersion of Plane Elastic-Waves by a Slender Body with Free-Boundary”, 270, no. 6, 1983, 1300–1305  mathscinet  zmath  isi
    5. Boiko A., “Scattering of Plane-Waves by a Slender Body of Revolution”, 29, no. 3, 1983, 189–191  mathscinet  isi
    6. V. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii, “Asymptotic expansions of the eigenvalues of boundary value problems for the Laplace operator in domains with small holes”, Math. USSR-Izv., 24:2 (1985), 321–345  mathnet  crossref  mathscinet  zmath
    7. Kiselev A., “Thin Cylindrical Emitter in Inhomogeneous Elastic Medium”, Zhurnal Tek. Fiz., 54:2 (1984), 209–215  mathscinet  isi
    8. Maslennikova G., “A Neumann Problem for the Helmholtz Operator in the Exterior to a Thin Body of Revolution”, Differ. Equ., 20:2 (1984), 251–259  mathnet  mathscinet  isi
    9. Zhdanova G., “Dirichlet Problem for the Helmholtz Operator in the Exterior of a Thin Body of Revolution”, Differ. Equ., 20:8 (1984), 1036–1042  mathnet  mathscinet  zmath  isi
    10. 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
    11. Boiko A., Maksimova N., “Diffraction of a Plane Sound-Wave by a Shell of Revolution”, 34, no. 1, 1988, 21–23  isi
    12. Boiko A., Tetyukhin M., “Diffraction of a Plane Sound-Wave by a Slender Elastic Body of Revolution with a Perfectly Rigid Inclusion”, 35, no. 1, 1989, 89–90  mathscinet  isi
    13. 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
    14. Boiko A., Tetyukhin M., “Scattering of Plane-Waves by a Thin Fluid Body of Revolution with a Fluid Inclusion”, 37, no. 1, 1991, 96–97  isi
    15. Boiko A., Dyshko A., Tetyukhin M., “Scattering of a Plane-Wave by an Acoustically Compliant Prolate Body of Revolution”, 38, no. 5, 1992, 456–460  isi
    16. Melnik T., Nazarov S., “The Asymptotic Structure of the Spectrum of the Problem on a Harmonically Oscillating Wheel-Boss with Hard Spokes”, Dokl. Akad. Nauk, 333:1 (1993), 13–15  mathnet  mathscinet  isi
    17. 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
    18. 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
    19. 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
    20. I. Yu. Popov, D. A. Zubok, “Two physical applications of the Laplace operator perturbed on a null set”, Theoret. and Math. Phys., 119:2 (1999), 629–639  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. Argatov I.I., “Extension of an elastic space with a rigid bar”, Journal of Applied Mechanics and Technical Physics, 49:1 (2008), 98–104  crossref  isi  elib
    22. Ivan I. Argatov, Federico J. Sabina, “Acoustic diffraction by a thin soft torus”, Wave Motion, 45:6 (2008), 846  crossref
    23. Ivan Argatov, Igor Sevostianov, “Rigid toroidal inhomogeneity in an elastic medium”, International Journal of Engineering Science, 49:1 (2011), 61  crossref
    24. A. A. Ershov, “Asimptotika resheniya vtoroi kraevoi zadachi dlya uravneniya Laplasa vne maloi okrestnosti otrezka”, Tr. IMM UrO RAN, 21, no. 1, 2015, 81–96  mathnet  mathscinet  elib
    25. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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