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Diffraction by a half-plane with different face impedances on an obstacle perpendicular to the boundary. (English) Zbl 1327.35074
Summary: The paper is devoted to study classes of plane wave diffraction problems by a region which involves a crack with impedance boundary conditions. Conditions on the wave number and impedance parameters are found to ensure the well-posedness of the problems in a scale of Bessel potential spaces. Under such conditions, representations of the solutions are also obtained upon the consideration of some associated operators which, in a sense, combine operators of Wiener-Hopf and Hankel type.
MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35C15 Integral representations of solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
35P25 Scattering theory for PDEs
47A20 Dilations, extensions, compressions of linear operators
47A53 (Semi-) Fredholm operators; index theories
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47G30 Pseudodifferential operators
78A45 Diffraction, scattering
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Full Text: Euclid