Communications in Mathematical Analysis

Diffraction by a Half-plane with Different Face Impedances on an Obstacle Perpendicular to the Boundary

L. P. Castro and D. Kapanadze

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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.

Article information

Commun. Math. Anal., Volume 17, Number 2 (2014), 45-65.

First available in Project Euclid: 18 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35C15: Integral representations of solutions 35J25: Boundary value problems for second-order elliptic equations 35P25: Scattering theory [See also 47A40] 47A20: Dilations, extensions, compressions 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 47A68: Factorization theory (including Wiener-Hopf and spectral factorizations) 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 78A45: Diffraction, scattering [See also 34E20 for WKB methods]

Helmholtz equation wave diffraction impedance boundary value problems potential method oscillating symbols Wiener-Hopf operator Hankel operator


Castro, L. P.; Kapanadze, D. Diffraction by a Half-plane with Different Face Impedances on an Obstacle Perpendicular to the Boundary. Commun. Math. Anal. 17 (2014), no. 2, 45--65.

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