The direct scattering problem for penetrable obstacles included in a cavity

Xianghe Zhu (), Chaoquan Peng () and Jun Guo ()
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Xianghe Zhu: Renmin University of China
Chaoquan Peng: South-Central University For Nationalities
Jun Guo: South-Central University For Nationalities

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 313-322

Abstract: Abstract We consider the problem of interior scattering from a point source for a bounded domain D containing two penetrable scatterers $$\Omega _1$$ Ω 1 and $$\Omega _2$$ Ω 2 in $$R^2$$ R 2 . The integral representation for a solution is reconstructed in the form of special combined potentials. The density functions included in the potentials satisfy the uniquely solvable Riesz-Fredholm integral equation. Then we obtain the existence and uniqueness of the solution for the direct scattering problem.

Keywords: Boundary integral equation; Helmholtz equation; Mixed potentials; Riesz-Fredholm theory; 35J05; 45B07 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00141-5

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