Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On a uniquely solvable integral equation in a mixed Dirichlet-Neumann problem of acoustic scattering

Author: P. A. Krutitskii
Journal: Quart. Appl. Math. 59 (2001), 493-506
MSC: Primary 45B05; Secondary 31B20, 35J05, 35J25, 76Q05
DOI: https://doi.org/10.1090/qam/1848531
MathSciNet review: MR1848531
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Abstract: The mixed Dirichlet--Neumann problem for the Helmholtz equation in the exterior of several bodies (obstacles) is studied in 2 and 3 dimensions. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called the ``method of interior boundaries", because additional boundaries are introduced inside scattering bodies, where the Neumann boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact, our method holds for any positive wave numbers. The Neumann and Dirichlet problems are particular cases of our problem.

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DOI: https://doi.org/10.1090/qam/1848531
Article copyright: © Copyright 2001 American Mathematical Society

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