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

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

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

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Abstract

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.