Lyalinov, M. A.; Vardapetyan, L. G. Diffraction of a plane electromagnetic wave obliquely incident upon the edge of a wedge with a dielectric coating. (English. Russian original) Zbl 0933.78005 J. Math. Sci., New York 86, No. 3, 2705-2720 (1997); translation from Zap. Nauchn. Semin. POMI 218, 72-95 (1994). Summary: The diffraction of a plane electromagnetic wave obliquely incident upon the edge of a coated wedge is considered. The generalized impedance boundary conditions (GIBC’s) on the wedge’s faces are used to simulate the effect of the coatings. To insure the well-posedness of the problem, special contact conditions (CC’s) on the edge are additionally imposed. By using Sommerfeld integrals, the problem is reduced to a system of coupled functional equations, which is solved by the perturbation method. It is shown that, for a certain range of the angles of oblique incidence, the solution can be represented in the form of convergent series that are Neumann series for linear equations with contracting operators. Nonuniform asymptotics of the wave field for regions outside a neighborhood of the edge of the wedge are constructed. Cited in 1 Document MSC: 78A45 Diffraction, scattering 39B05 General theory of functional equations and inequalities Keywords:infinite metal wedge; thin coating; generalized impedance boundary conditions; Sommerfeld integrals; system of coupled functional equations; perturbation method; Neumann series; diffraction; plane electromagnetic wave Citations:Zbl 0924.00023 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Maliužinec, G. D., Excitation, reflection, and emission of surface waves from a wedge with given face impedances, Soviet Phys. Dokl., 3, 752-755 (1958) · Zbl 0089.44202 [2] Senior, T. B. A., Diffraction by a generalized impedance half-plane, Radio Science, 26, 163-167 (1991) [3] Bernard, J.-M. L., Diffraction by a metallic wedge covered with a dielectric material, Wave-Motion, 9, 543-561 (1987) · Zbl 0621.73028 [4] Bernard, J.-M. L., On the diffraction of an electromagnetic skew incident wave by a non-perfectly conducting wedge, Ann. Telecommun., 45, 30-39 (1990) [5] Osypov, A. V., General solution for a class of diffraction problems, J. Phys. A: Math. Gen., 27, L27-L32 (1994) · Zbl 0824.76079 [6] I. V. Andronov, B. P. Belinskii, V. S. Buldyrev, and M. A. Lyalinov, “Problems of electrodynamics and acoustics with generalized impedance boundary conditions that have discontinuous coefficients or singular points,” in:Proceedings of X School-Seminar on Diffraction and Wave Propagation, Moscow (1993), pp. 5-30. [7] Lyalinov, M. A., On one approach to an electromagnetic diffraction problem in a wedge-shaped region, J. Phys. A: Math. Gen., 27, L183-L189 (1994) · Zbl 0850.78008 · doi:10.1088/0305-4470/27/6/006 [8] Tužilin, A. A., Diffraction of a plane sonic wave in an angular domain with absolutely rigid and slippery faces coated with thin elastic plates, Differents. Uravn., 9, 1876-1888 (1973) [9] Tužilin, A. A., On the theory of Maliužinec’s inhomogeneous functional equations, Differents. Uravn., 9, 2058-2064 (1973) · Zbl 0287.39002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.