Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel

Paweł Wójcik; Michail A. Sheshko; Dorota Pylak; Paweł Karczmarek

Annales UMCS, Mathematica (2012)

  • Volume: 66, Issue: 2, page 93-105
  • ISSN: 2083-7402

Abstract

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In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.

How to cite

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Paweł Wójcik, et al. "Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel." Annales UMCS, Mathematica 66.2 (2012): 93-105. <http://eudml.org/doc/268054>.

@article{PawełWójcik2012,
abstract = {In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.},
author = {Paweł Wójcik, Michail A. Sheshko, Dorota Pylak, Paweł Karczmarek},
journal = {Annales UMCS, Mathematica},
keywords = {Singular integral equations; Cauchy-type kernel; multiplicative kernel; logarithmic singularities.; singular integral equations; logarithmic singularities},
language = {eng},
number = {2},
pages = {93-105},
title = {Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel},
url = {http://eudml.org/doc/268054},
volume = {66},
year = {2012},
}

TY - JOUR
AU - Paweł Wójcik
AU - Michail A. Sheshko
AU - Dorota Pylak
AU - Paweł Karczmarek
TI - Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
JO - Annales UMCS, Mathematica
PY - 2012
VL - 66
IS - 2
SP - 93
EP - 105
AB - In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.
LA - eng
KW - Singular integral equations; Cauchy-type kernel; multiplicative kernel; logarithmic singularities.; singular integral equations; logarithmic singularities
UR - http://eudml.org/doc/268054
ER -

References

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  1. [1] Bisplinghoff, R. L., Ashley, H. and Halfman, R. L., Aeroelasticity, Dover Publications, Mineola, 1996. 
  2. [2] Gakhov, F. D., Boundary Value Problems, Nauka, Moscow, 1977. Zbl0449.30030
  3. [3] Karczmarek, P., Singular integral equation with a multiplicative Cauchy kernel in thehalf-plane, Opuscula Math. 28 (2008), 63-72. Zbl1180.45001
  4. [4] Karczmarek, P., Pylak, D., Wójcik, P., Singular integral equations with multiplicativeCauchy-type kernels, Fasc. Math. 50 (2013), in press. Zbl1292.45004
  5. [5] Lifanov, I. K., Singular Integral Equations and Discrete Vortices, VSP, Utrecht, 1996. Zbl0871.65110
  6. [6] Muskhelishvili, N. I., Singular Integral Equations. Boundary Problems of FunctionTheory and Their Application to Mathematical Physics, Dover Publications, Inc., Mineola, New York, 2008. 
  7. [7] Pylak, D., Approximate solutions of a singular integral equation with Cauchy kernelin the quarter plane, Opuscula Math. 28 (2008), 179-194. Zbl1161.65095
  8. [8] Pylak, D., Sheshko, M. A., Inversion of singular integrals with Cauchy kernels in thecase of an infinite integration domain, Differ. Equ. 41 (2005), 1297-1310. Zbl1128.45001
  9. [9] Sheshko, M., Singular Integral Equations with Cauchy and Hilbert Kernels and TheirsApproximated Solutions, TN KUL, Lublin, 2003. 
  10. [10] Sheshko, M. A., Sheshko, S. M., Inversion of singular integrals with multiplicativeCauchy kernel and infinite integration domain, Differ. Equ. 47 (2011), 534-546.[WoS] Zbl1235.45001

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