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Boundary Hypersingular Integral Delay Equation for Nonstationary Problems of Scattering by Perfectly Conducting Bodiesстатья
- Авторы: Samokhin A.B., Setukha A.V.
- Журнал: Differential Equations
- Том: 58
- Номер: 8
- Год издания: 2022
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1082
- Последняя страница: 1096
- DOI: 10.1134/s0012266122080092
- Аннотация: We consider the application of the method of boundary integral equations to the problem of scattering of an electromagnetic field obeying the nonstationary Maxwell equations by a system of perfectly conducting objects. An integral representation of the electromagnetic field in terms of surface currents is used. The main result of the paper is the proof of the existence of boundary values for the electric field defined by such an integral representation that are expressed via a hypersingular integral understood in the sense of the Hadamard finite part. This permits reducing the problem to an integro-differential equation of evolution type with delay containing a hypersingular surface integral. It is also proved that if this equation has a solution in a certain function class, then the electric and magnetic fields determined by the corresponding integral representations are a solution of the original scattering problem for Maxwell’s equations.
- Добавил в систему: Сетуха Алексей Викторович