Geodesic
Some features of second kind Fredholm equations kernels
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 28-33.

Voir la notice de l'article provenant de la source Math-Net.Ru

Kernels of Fredholm integral equations of the second kind with exceptions are analysed in this article. The equations under consideration have a meaning of magnetic field boundary condition and are used in problems of scattering on scatterers with finite thickness. It is shown that these kernels could be stated in a form of Dirac delta-functions. This mathematical formalization results in interesting physical effect that induced current calculated via physical optics equals the difference of face and back currents of the scatterer, calculated using method of integral equations.
Keywords: integral equations, scattering problem for electromagnetic fields, Dirac delta function. 
@article{VSGTU_2011_1_a3,
     author = {M. A. Buzova},
     title = {Some features of second kind {Fredholm} equations kernels},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {28--33},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a3/}
}
TY  - JOUR
AU  - M. A. Buzova
TI  - Some features of second kind Fredholm equations kernels
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2011
SP  - 28
EP  - 33
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a3/
LA  - ru
ID  - VSGTU_2011_1_a3
ER  - 
%0 Journal Article
%A M. A. Buzova
%T Some features of second kind Fredholm equations kernels
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2011
%P 28-33
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a3/
%G ru
%F VSGTU_2011_1_a3
M. A. Buzova. Some features of second kind Fredholm equations kernels. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 28-33. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a3/

[1] Vasil'ev E. N., Excitation of Bodies of Rotation, Radio i Svyaz', Moscow, 1987, 272 pp.

[2] Computer Techniques for Electromagnetics, International series of monographs in electrical engineering, 7, ed. R. Mittra, Wiley, Oxford – New York – Toronto – Sydney – Braunschweig, 1973, 403 pp. ; Vychislitelnye metody v elektrodinamike, ed. R. Mittra, Mir, M., 1977, 487 pp. | MR | MR

[3] Kupradze V. D., Boundary Value Problems in the Theory of Oscillations and Integral Equations, Gostekhizdat, Moscow – Leningrad, 1951, 280 pp. | MR

[4] Buzova M. A., “Main principles to combine the physical optics methods and integral equations for electrodynamic analysis of electrically extended surface diffusers”, Vestnik Samarskogo otraslevogo nauchno-issledovatel'skogo instituta radio, 2007, no. 3(17), 44–50

[5] Buzova M. A., “Second kind integral equation and Huygens–Kirchhoff approximation in the problems of electromagnetic field scattering on lengthy perfectly conducting scatters”, Dokl. Physics, 55:4 (2010), 164–167 | DOI | MR | Zbl