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Acoustic scattering by an inhomogeneous layer on a rigid plate

Zhang, B. and Chandler-Wilde, S. N. (1998) Acoustic scattering by an inhomogeneous layer on a rigid plate. SIAM Journal on Applied Mathematics (SIAP), 58 (6). pp. 1931-1950. ISSN 0036-1399

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To link to this item DOI: 10.1137/S0003613999631269


The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Item Type:Article
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:32654
Publisher:Society for Industrial and Applied Mathematics


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