KFU. Card publication. Boundary-Value Problems for the Helmholtz Equation for a Half-Plane with a Lipschitz Inclusion

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BOUNDARY-VALUE PROBLEMS FOR THE HELMHOLTZ EQUATION FOR A HALF-PLANE WITH A LIPSCHITZ INCLUSION

Form of presentation

Articles in Russian journals and collections

Year of publication

2018

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Authors, employees of KFU

Lipachev Evgeniy Konstantinovich, author

Bibliographic description in the original language

Lipachev E.K. Boundary-Value Problems for the Helmholtz Equation for a Half-Plane with a Lipschitz Inclusion / E.K.Lipachev // Lobachevskii Journal of Mathematics, 2018, Vol. 39, No. 5, pp. 698–705. https://doi.org/10.1134/S1995080218050104.

Annotation

I consider the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. Boundary value problems, modeling the process of wave diffraction, are constructed in the form of Helmholtz equations and boundary conditions on the boundary, formulated in terms of traces, as well as the radiation conditions at infinity. I carry out research on these problems in generalized Sobolev spaces. I proved the solvability of the boundary value problems of Dirichlet and Neumann. I have obtained solutions of boundary value problems in the form of functions that by their properties are analogs of the classical potentials of single and double layers. Boundary problems are reduced to integral equations of the second kind.

Keywords

Lipschitz domains, Helmholtz equation, layer potentials, Dirichlet problem, Neumann problem, Boundary Integral Equations.

The name of the journal

Lobachevskii Journal of Mathematics

URL

https://link.springer.com/article/10.1134%2FS1995080218050104

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=186617&p_lang=2

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Full metadata record

Field DC	Value	Language
dc.contributor.author	Lipachev Evgeniy Konstantinovich	ru_RU
dc.date.accessioned	2018-01-01T00:00:00Z	ru_RU
dc.date.available	2018-01-01T00:00:00Z	ru_RU
dc.date.issued	2018	ru_RU
dc.identifier.citation	Lipachev E.K. Boundary-Value Problems for the Helmholtz Equation for a Half-Plane with a Lipschitz Inclusion / E.K.Lipachev // Lobachevskii Journal of Mathematics, 2018, Vol. 39, No. 5, pp. 698–705. https://doi.org/10.1134/S1995080218050104.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=186617&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	I consider the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. Boundary value problems, modeling the process of wave diffraction, are constructed in the form of Helmholtz equations and boundary conditions on the boundary, formulated in terms of traces, as well as the radiation conditions at infinity. I carry out research on these problems in generalized Sobolev spaces. I proved the solvability of the boundary value problems of Dirichlet and Neumann. I have obtained solutions of boundary value problems in the form of functions that by their properties are analogs of the classical potentials of single and double layers. Boundary problems are reduced to integral equations of the second kind.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Lipschitz domains	ru_RU
dc.subject	Helmholtz equation	ru_RU
dc.subject	layer potentials	ru_RU
dc.subject	Dirichlet problem	ru_RU
dc.subject	Neumann problem	ru_RU
dc.subject	Boundary Integral Equations.	ru_RU
dc.title	Boundary-Value Problems for the Helmholtz Equation for a Half-Plane with a Lipschitz Inclusion	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU