Theory of Integral Equations for Axisymmetric Scattering by a Disk

Autor:	S. I. Eminov
Rok vydání:	2019
Předmět:	Computational Mathematics Matrix (mathematics) Invertible matrix Positive definiteness law Operator (physics) Mathematical analysis Identity matrix Orthonormal basis Compact operator Integral equation law.invention Mathematics
Zdroj:	Computational Mathematics and Mathematical Physics. 59:1372-1379
ISSN:	1555-6662 0965-5425
DOI:	10.1134/s0965542519080177
Popis:	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.
Databáze:	OpenAIRE
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