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, Tome 66 (2012), p. 93-105 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:268054
@article{bwmeta1.element.doi-10_2478_v10062-012-0016-y,
     author = {Pawe\l\ W\'ojcik and Michail A. Sheshko and Dorota Pylak and Pawe\l\ Karczmarek},
     title = {Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel},
     journal = {Annales UMCS, Mathematica},
     volume = {66},
     year = {2012},
     pages = {93-105},
     zbl = {1297.45005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0016-y}
}
Paweł Wójcik; Michail A. Sheshko; Dorota Pylak; Paweł Karczmarek. Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel. Annales UMCS, Mathematica, Tome 66 (2012) pp. 93-105. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0016-y/

[1] Bisplinghoff, R. L., Ashley, H. and Halfman, R. L., Aeroelasticity, Dover Publications, Mineola, 1996.

[2] Gakhov, F. D., Boundary Value Problems, Nauka, Moscow, 1977. | Zbl 0449.30030

[3] Karczmarek, P., Singular integral equation with a multiplicative Cauchy kernel in thehalf-plane, Opuscula Math. 28 (2008), 63-72. | Zbl 1180.45001

[4] Karczmarek, P., Pylak, D., Wójcik, P., Singular integral equations with multiplicativeCauchy-type kernels, Fasc. Math. 50 (2013), in press. | Zbl 1292.45004

[5] Lifanov, I. K., Singular Integral Equations and Discrete Vortices, VSP, Utrecht, 1996. | Zbl 0871.65110

[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] Pylak, D., Approximate solutions of a singular integral equation with Cauchy kernelin the quarter plane, Opuscula Math. 28 (2008), 179-194. | Zbl 1161.65095

[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. | Zbl 1128.45001

[9] Sheshko, M., Singular Integral Equations with Cauchy and Hilbert Kernels and TheirsApproximated Solutions, TN KUL, Lublin, 2003.

[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] | Zbl 1235.45001