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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 8, Pages 1431–1438 (Mi zvmmf10944)  

Theory of integral equations for axisymmetric scattering by a disk

S. I. Èminov

Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, 173003 Russia

Abstract: A theory of integral equations for radial currents in the axisymmetric problem of scattering by a disk is constructed. The theory relies on the extraction of the principal part of a continuously invertible operator and on the proof of its positive definiteness. Existences and uniqueness theorems are obtained for the problem. An orthonormal basis is constructed for the energy space of the positive definite operator. Each element of the basis on the boundary behaves in the same manner as the unknown function. The structure of the matrix of the integral operator in this basis is studied. It is found that the principal part has an identity matrix, while the matrix of the next operator is tridiagonal.

Key words: scattering by a disk, continuously invertible operator, positive definite operator, Hankel transform, compact operator, orthonormal basis, associated Legendre functions of the first kind, operator matrix.

DOI: https://doi.org/10.1134/S0044466919080180


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:8, 1372–1379

Bibliographic databases:

UDC: 621.396:517.9
Received: 01.04.2019
Revised: 01.04.2019
Accepted:10.04.2019

Citation: S. I. Èminov, “Theory of integral equations for axisymmetric scattering by a disk”, Zh. Vychisl. Mat. Mat. Fiz., 59:8 (2019), 1431–1438; Comput. Math. Math. Phys., 59:8 (2019), 1372–1379

Citation in format AMSBIB
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