Paper Info
Title
Acoustic scattering by an inhomogeneous layer on a rigid plate
Abstract
The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R-2 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.
Year
DOI
Venue
1998
10.1137/S0003613999631269
SIAM Journal of Applied Mathematics
Keywords
Field
DocType
radiation condition,rough surface scattering,inhomogeneous layer,integral equations,existence,uniqueness,guided waves,Neumann condition
Rayleigh scattering,Uniqueness,Mathematical optimization,Mathematical analysis,Wavenumber,Integral equation,Scattering,Wave equation,Guided wave testing,Acoustic wave,Mathematics
Journal
Volume
Issue
ISSN
58
6
0036-1399
Citations 
PageRank 
References 
12
3.76
0
Authors
2
Name
Order
Citations
PageRank
Bo Zhang1168.04
Simon N. Chandler-Wilde211616.79