On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics

Autores
Douglas, Jim; Santos, Juan Enrique; Sheen, Dongwoo
Año de publicación
2000
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We analyze the solution of the time-harmonic Maxwell equations with vanishing electric permittivity in bounded domains and subject to absorbing boundary conditions. The problem arises naturally in magnetotellurics when considering the propagation of electromagnetic waves within the earth's interior. Existence and uniqueness are shown under the assumption that the source functions are square integrable. In this case, the electric and magnetic fields belong to H(curl; Ω). If, in addition, the divergences of the source functions are square integrable and the coefficients are Lipschitz-continuous, a stronger regularity result is obtained. A decomposition of the space of square integrable vector functions and a new compact imbedding result are exploited.
Fil: Douglas, Jim. Purdue University; Estados Unidos
Fil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Purdue University; Estados Unidos
Fil: Sheen, Dongwoo. Seoul National University; Kazajistán
Materia
Solution
Uniqueness
Equation
Magneoteluric
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/71631
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotelluricsDouglas, JimSantos, Juan EnriqueSheen, DongwooSolutionUniquenessEquationMagneotelurichttps://purl.org/becyt/ford/1.5https://purl.org/becyt/ford/1We analyze the solution of the time-harmonic Maxwell equations with vanishing electric permittivity in bounded domains and subject to absorbing boundary conditions. The problem arises naturally in magnetotellurics when considering the propagation of electromagnetic waves within the earth's interior. Existence and uniqueness are shown under the assumption that the source functions are square integrable. In this case, the electric and magnetic fields belong to H(curl; Ω). If, in addition, the divergences of the source functions are square integrable and the coefficients are Lipschitz-continuous, a stronger regularity result is obtained. A decomposition of the space of square integrable vector functions and a new compact imbedding result are exploited.Fil: Douglas, Jim. Purdue University; Estados UnidosFil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Purdue University; Estados UnidosFil: Sheen, Dongwoo. Seoul National University; KazajistánWorld Scientific2000-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/71631Douglas, Jim; Santos, Juan Enrique; Sheen, Dongwoo; On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics; World Scientific; Mathematical Models And Methods In Applied Sciences; 10; 4; 2-2000; 615-6280218-2025CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202500000331info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218202500000331info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:43:03Zoai:ri.conicet.gov.ar:11336/71631instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:43:03.359CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
title On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
spellingShingle On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
Douglas, Jim
Solution
Uniqueness
Equation
Magneoteluric
title_short On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
title_full On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
title_fullStr On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
title_full_unstemmed On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
title_sort On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics
dc.creator.none.fl_str_mv Douglas, Jim
Santos, Juan Enrique
Sheen, Dongwoo
author Douglas, Jim
author_facet Douglas, Jim
Santos, Juan Enrique
Sheen, Dongwoo
author_role author
author2 Santos, Juan Enrique
Sheen, Dongwoo
author2_role author
author
dc.subject.none.fl_str_mv Solution
Uniqueness
Equation
Magneoteluric
topic Solution
Uniqueness
Equation
Magneoteluric
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.5
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We analyze the solution of the time-harmonic Maxwell equations with vanishing electric permittivity in bounded domains and subject to absorbing boundary conditions. The problem arises naturally in magnetotellurics when considering the propagation of electromagnetic waves within the earth's interior. Existence and uniqueness are shown under the assumption that the source functions are square integrable. In this case, the electric and magnetic fields belong to H(curl; Ω). If, in addition, the divergences of the source functions are square integrable and the coefficients are Lipschitz-continuous, a stronger regularity result is obtained. A decomposition of the space of square integrable vector functions and a new compact imbedding result are exploited.
Fil: Douglas, Jim. Purdue University; Estados Unidos
Fil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Purdue University; Estados Unidos
Fil: Sheen, Dongwoo. Seoul National University; Kazajistán
description We analyze the solution of the time-harmonic Maxwell equations with vanishing electric permittivity in bounded domains and subject to absorbing boundary conditions. The problem arises naturally in magnetotellurics when considering the propagation of electromagnetic waves within the earth's interior. Existence and uniqueness are shown under the assumption that the source functions are square integrable. In this case, the electric and magnetic fields belong to H(curl; Ω). If, in addition, the divergences of the source functions are square integrable and the coefficients are Lipschitz-continuous, a stronger regularity result is obtained. A decomposition of the space of square integrable vector functions and a new compact imbedding result are exploited.
publishDate 2000
dc.date.none.fl_str_mv 2000-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/71631
Douglas, Jim; Santos, Juan Enrique; Sheen, Dongwoo; On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics; World Scientific; Mathematical Models And Methods In Applied Sciences; 10; 4; 2-2000; 615-628
0218-2025
CONICET Digital
CONICET
url http://hdl.handle.net/11336/71631
identifier_str_mv Douglas, Jim; Santos, Juan Enrique; Sheen, Dongwoo; On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics; World Scientific; Mathematical Models And Methods In Applied Sciences; 10; 4; 2-2000; 615-628
0218-2025
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202500000331
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218202500000331
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846082934433382400
score 13.22299

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