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

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.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:1, 145–161

Bibliographic databases:

UDC: 517.9
MSC: 35J05, 35B40

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
Related articles on Google Scholar: Russian articles, English articles

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
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
3. Zorin I., Nazarov S., “Strain-Stress State Asymptotics of Elastic Space with a Rigid Toroidal Inclusion”, 272, no. 6, 1983, 1340–1343
4. Zhdanova G., “Dispersion of Plane Elastic-Waves by a Slender Body with Free-Boundary”, 270, no. 6, 1983, 1300–1305
5. Boiko A., “Scattering of Plane-Waves by a Slender Body of Revolution”, 29, no. 3, 1983, 189–191
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
7. Kiselev A., “Thin Cylindrical Emitter in Inhomogeneous Elastic Medium”, Zhurnal Tek. Fiz., 54:2 (1984), 209–215
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
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
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
11. Boiko A., Maksimova N., “Diffraction of a Plane Sound-Wave by a Shell of Revolution”, 34, no. 1, 1988, 21–23
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
13. S. A. Nazarov, “Asymptotic solution of a variational inequality modelling a friction”, Math. USSR-Izv., 37:2 (1991), 337–369
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
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
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
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
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
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
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
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
22. Ivan I. Argatov, Federico J. Sabina, “Acoustic diffraction by a thin soft torus”, Wave Motion, 45:6 (2008), 846
23. Ivan Argatov, Igor Sevostianov, “Rigid toroidal inhomogeneity in an elastic medium”, International Journal of Engineering Science, 49:1 (2011), 61
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
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
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