Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain (Q2187405)
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| English | Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain |
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Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain (English)
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2 June 2020
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The goal of the paper is to correct the fatal error made in the authors' previous paper [Georgian Math. J. 20, No. 3, 439--467 (2013; Zbl 1279.35014)]. Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain are studied by using the potential method. The problem with complex wave number is reduced to an equivalent, Mellin convolution-type boundary integral equation in the Sobolev-Slobodecki space on a semi-infinite axis. Then unique solvability criteria (Fredholm criteria) of the above mentioned mixed problems are obtained in classical finite energy space.
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model BVP
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Helmholtz equation
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angular domain
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mixed problem
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Dirichlet problem
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Neumann problem
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potential method
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boundary integral equation
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Mellin convolution equation
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Bessel potential space
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