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http://bura.brunel.ac.uk/handle/2438/16768
Title: | Singular Localised Boundary-Domain Integral Equations of Acoustic Scattering by Inhomogeneous Anisotropic Obstacle |
Authors: | Chkadua, O Mikhailov, SE Natroshvili, D |
Keywords: | Acoustic scattering;partial differential equations;transmission problems;localized parametrix |
Issue Date: | 2018 |
Publisher: | Wiley |
Citation: | Mathematical Methods in the Applied Sciences, pp. 1 - 25 |
Abstract: | We consider the time-harmonic acoustic wave scattering by a bounded anisotropic inhomogeneity embedded in an unbounded anisotropic homogeneousmedium. The materialparametersmay have discontinuitiesacross the interfacebetween the inhomogeneous interior and homogeneous exterior regions. The corresponding mathematicalproblemis formulatedas a transmissionproblemsfora secondorderelliptic partial differential equation of Helmholtz type with discontinuous variable coefficients. Using a localised quasi-parametrix based on the harmonic fundamental solution, the transmission problem for arbitrary values of the frequency parameter is reduced equivalently to a system of singular localised boundary-domain integral equations. Fredholm properties of the corresponding localised boundarydomainintegral operatorarestudiedanditsinvertibilityisestablishedinappropriate Sobolev-Slobodetskii and Bessel potential spaces, which implies existence and uniquenessresults for the localised boundary-domainintegralequationssystem and the correspondingacoustic scattering transmission problem. |
URI: | http://bura.brunel.ac.uk/handle/2438/16768 |
DOI: | https://doi.org/10.1002/mma.5268 |
ISSN: | 0170-4214 |
Appears in Collections: | Dept of Mathematics Research Papers |
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