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

• Autorzy: Paweł Wójcik , Michail A. Sheshko , Dorota Pylak , Paweł Karczmarek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Singular integral equations; Cauchy-type kernel; multiplicative kernel; logarithmic singularities

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2012
• Tom: 66
• Numer: 2

Daty

wydano

2012

online

2016-07-25

Twórcy

autor

Paweł Wójcik

autor

Michail A. Sheshko

autor

Dorota Pylak

autor

Paweł Karczmarek

Bibliografia

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• Karczmarek, P., Singular integral equation with a multiplicative Cauchy kernel in the half-plane, Opuscula Math. 28 (2008), 63-72.
• Karczmarek, P., Pylak, D., Wójcik, P., Singular integral equations with multiplicative Cauchy-type kernels, Fasc. Math. 50 (2013), in press.
• Lifanov, I. K., Singular Integral Equations and Discrete Vortices, VSP, Utrecht, 1996.
• Muskhelishvili, N. I., Singular Integral Equations. Boundary Problems of Function Theory and Their Application to Mathematical Physics, Dover Publications, Inc., Mineola, New York, 2008.
• Pylak, D., Approximate solutions of a singular integral equation with Cauchy kernel in the quarter plane, Opuscula Math. 28 (2008), 179-194.
• Pylak, D., Sheshko, M. A., Inversion of singular integrals with Cauchy kernels in the case of an infinite integration domain, Differ. Equ. 41 (2005), 1297-1310.
• Sheshko, M., Singular Integral Equations with Cauchy and Hilbert Kernels and Theirs Approximated Solutions, TN KUL, Lublin, 2003.
• Sheshko, M. A., Sheshko, S. M., Inversion of singular integrals with multiplicative Cauchy kernel and infinite integration domain, Differ. Equ. 47 (2011), 534-546.

Identyfikatory

DOI

10.17951/a.2012.66.2.93-105