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EXISTENCE AND UNIQUENESS THEOREMS IN ELECTROMAGNETIC DIFFRACTION ON SYSTEMS OF LOSSLESS DIELECTRICS AND PERFECTLY CONDUCTING SCREENSстатья
- Авторы: Smirnov Y.G., Tsupak A.A.
- Журнал: Applicable Analysis
- Том: 96
- Номер: 8
- Год издания: 2017
- Издательство: Taylor & Francis
- Местоположение издательства: United Kingdom
- Первая страница: 1326
- Последняя страница: 1341
- DOI: 10.1080/00036811.2016.1188289
- Аннотация: New vector problem of electromagnetic wave diffraction by a system of non-intersecting three-dimensional inhomogeneous dielectric bodies and infinitely thin screens is considered in a quasiclassical formulation as well as the classical problem of diffraction by a lossless inhomogeneous body. In both cases, the original boundary value problem for Maxwell’s equations is reduced to integro-differential equations in the regions occupied by the bodies (and on the screen surfaces). The integro-differential operator is treated as a pseudodifferential operator in Sobolev spaces and is shown to be zero-index Fredholm operator. Uniqueness of solutions is proved under the realistic hypothesis of discontinuity of the dielectric permittivity the boundary of a volume scatterer. This result allowed to establish invertibility of the integro-differential operator in sufficiently broad spaces. For the problem of diffraction on dielectrics and surface conductors, theorem on smoothness of a solution is proved under assumption of data smoothness. The latter implies equivalence between the differential and integral formulations of the scattering problem. The matrix integro-differential operator is proved to be a Fredholm invertible operator. Thus, the existence of a unique solution to both problems is established.
- Добавил в систему: Цупак Алексей Александрович