Integro-differential equations with singular and hypersingular integrals
https://doi.org/10.29235/1561-2430-2018-54-4-404-407
Abstract
Quadrature linear integro-differential equations on a closed curve located in the complex plane are solved. The equations contain singular integrals which are understood in the sense of the main value and hypersingular integrals which are understood in the sense of the Hadamard finite part. The coefficients of the equations have a special structure.
About the Authors
E. I. Zverovich
Belarusian State University
Belarus
D. Sc. (Physics and Mathematics), Professor, Professor of the Department of Function Theory
Belarus
D. Sc. (Physics and Mathematics), Professor, Professor of the Department of Function Theory
A. P. Shilin
Belarusian State University
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor, Assistant Professor of the Department of Higher Mathematics and Mathematical Physics
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor, Assistant Professor of the Department of Higher Mathematics and Mathematical Physics
References
1. Zverovich E. I. Solution of the hypersingular integro-differential equation with constant coefficients. Doklady Nacionalnoi Akademii Nauk Belarusi = Proceedings of the National Academy of Sciences of Belarus, 2010, vol. 54, no. 6, pp. 5–8 (in Russian).
2. Zverovich E. I. Generalization of Sohotsky formulas. Vestsі Natsyyanal’nai akademіі navuk Belarusі. Seryya fіzіka matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series, 2012, no. 6, pp. 24–28 (in Russian).
3. Gakhov F. D. Boundary Value Problems. Moscow, Nauka Publ., 1977. 640 p. (in Russian).
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