A wave diffraction problem with higher order impedance boundary conditions
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/35262 |
Resumo: | In this paper, we consider an impedance boundary transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. Operator theoretical methods and relations between operators are built to deal with the problem and, as consequence, a transparent interpretation of the problem in an operator theory framework are associated to the problem. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. At the end, we describe when the operators associated with the problem enjoy the Fredholm property in terms of the initial space order parameters. |
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A wave diffraction problem with higher order impedance boundary conditionsHelmholtz equationhigher order impedance boundary conditionBessel potential spaceconvolution type operatorFredholm operatorIn this paper, we consider an impedance boundary transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. Operator theoretical methods and relations between operators are built to deal with the problem and, as consequence, a transparent interpretation of the problem in an operator theory framework are associated to the problem. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. At the end, we describe when the operators associated with the problem enjoy the Fredholm property in terms of the initial space order parameters.NAUN2022-11-23T11:03:34Z2022-01-01T00:00:00Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/35262eng10.46300/9101.2022.16.12Simões, A. M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:07:54Zoai:ria.ua.pt:10773/35262Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:06:19.324502Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A wave diffraction problem with higher order impedance boundary conditions |
title |
A wave diffraction problem with higher order impedance boundary conditions |
spellingShingle |
A wave diffraction problem with higher order impedance boundary conditions Simões, A. M. Helmholtz equation higher order impedance boundary condition Bessel potential space convolution type operator Fredholm operator |
title_short |
A wave diffraction problem with higher order impedance boundary conditions |
title_full |
A wave diffraction problem with higher order impedance boundary conditions |
title_fullStr |
A wave diffraction problem with higher order impedance boundary conditions |
title_full_unstemmed |
A wave diffraction problem with higher order impedance boundary conditions |
title_sort |
A wave diffraction problem with higher order impedance boundary conditions |
author |
Simões, A. M. |
author_facet |
Simões, A. M. |
author_role |
author |
dc.contributor.author.fl_str_mv |
Simões, A. M. |
dc.subject.por.fl_str_mv |
Helmholtz equation higher order impedance boundary condition Bessel potential space convolution type operator Fredholm operator |
topic |
Helmholtz equation higher order impedance boundary condition Bessel potential space convolution type operator Fredholm operator |
description |
In this paper, we consider an impedance boundary transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. Operator theoretical methods and relations between operators are built to deal with the problem and, as consequence, a transparent interpretation of the problem in an operator theory framework are associated to the problem. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. At the end, we describe when the operators associated with the problem enjoy the Fredholm property in terms of the initial space order parameters. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-11-23T11:03:34Z 2022-01-01T00:00:00Z 2022 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/35262 |
url |
http://hdl.handle.net/10773/35262 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.46300/9101.2022.16.12 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
NAUN |
publisher.none.fl_str_mv |
NAUN |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137718119170049 |