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Mat. Sb., 2001, Volume 192, Number 8, Pages 3–46 (Mi msb584)  

This article is cited in 8 scientific papers (total in 8 papers)

On certain one- and two-dimensional hypersingular integral equations

A. Yu. Anfinogenova, I. K. Lifanova, P. I. Lifanovb

a N.E. Zhukovsky Military Engineering Academy
b Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: For two-dimensional singular and hypersingular integrals more general definitions than the traditional ones are introduced. For a hypersingular operator on a sphere a new spectral relation is obtained. Quadrature formulae of the kind of discrete vortex pairs for one-dimensional and of the kind of closed vortex frames for two-dimensional hypersingular integrals are considered; questions on their convergence are discussed, as well as the convergence of numerical solutions to the corresponding hypersingular integral equations on a finite line interval and a circle. An experiment on the numerical solution of a hypersingular integral equation on a sphere is carried out, which demonstrates analogies between numerical solutions of hypersingular integral equations on a finite interval and a sphere.

DOI: https://doi.org/10.4213/sm584

Full text: PDF file (461 kB)
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English version:
Sbornik: Mathematics, 2001, 192:8, 1089–1131

Bibliographic databases:

UDC: 517.5
MSC: 45E10, 65R20
Received: 25.12.2000

Citation: A. Yu. Anfinogenov, I. K. Lifanov, P. I. Lifanov, “On certain one- and two-dimensional hypersingular integral equations”, Mat. Sb., 192:8 (2001), 3–46; Sb. Math., 192:8 (2001), 1089–1131

Citation in format AMSBIB
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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. G. M. Vainikko, N. V. Lebedeva, I. K. Lifanov, “Numerical solution of a singular and a hypersingular integral equation on an interval and the delta function”, Sb. Math., 193:10 (2002), 1397–1410  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Vainikko G.M., Lifanov I.K., “A study of divergent integrals”, Dokl. Math., 67:2 (2003), 237–241  mathnet  mathscinet  zmath  isi  elib
    3. Lifanov I.K., Poltavskii L.N., “Numerical solution of a hypersingular integral equation on the torus”, Differ. Equ., 39:9 (2003), 1316–1331  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. G. M. Vainikko, I. K. Lifanov, “Approaches to the summability of divergent multidimensional integrals”, Sb. Math., 194:8 (2003), 1137–1166  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Sundaram N., Farris T.N, “The generalized advancing conformal contact problem with friction, pin loads and remote loading – Case of rigid pin”, International Journal of Solids and Structures, 47:6 (2010), 801–815  crossref  zmath  isi  elib  scopus  scopus  scopus
    6. Sundaram N., Farris T.N., “Mechanics of advancing pin-loaded contacts with friction”, Journal of the Mechanics and Physics of Solids, 58:11 (2010), 1819–1833  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Aliev R.A., Gadjieva Ch.A., “Approximation of Hypersingular Integral Operators With Cauchy Kernel”, Numer. Funct. Anal. Optim., 37:9 (2016), 1055–1065  crossref  mathscinet  zmath  isi  scopus
    8. Gadjieva Ch.A., “A New Approximate Method For Solving Hypersingular Integral Equations With Hilbert”, Proc. Inst. Math. Mech., 43:2 (2017), 316–329  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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