Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da FURG (RI FURG) |
Texto Completo: | http://repositorio.furg.br/handle/1/3201 |
Resumo: | In this contribution we show sufficient conditions for simultaneous unique identification of unknown spacewise coefficients and heat source in a parabolic partial differential equation given additional final time measurements. Our approach is based on density, in suitable spaces, of the corresponding adjoint problem. A second issue of this paper is the regularization approach. The sequence of approximated solution is obtained by coupling the nonlinear Landweber iteration with iterated Tikhonov regularization. We show that the parameter-to-solution map satisfies sufficient conditions to prove stability and convergence of approximated solutions for the identification problem. We use a unified discrepancy principle as the stopping criteria. Finally, we apply the developed theory in the inverse identification problem of unknown parameters (perfusion coefficient, metabolic heat source) for the identification of tumor regions by thermography. |
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Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equationUniquenessThermophysical parameters and source identificationIterative regularizationParabolic type equationFinal time measurementsIn this contribution we show sufficient conditions for simultaneous unique identification of unknown spacewise coefficients and heat source in a parabolic partial differential equation given additional final time measurements. Our approach is based on density, in suitable spaces, of the corresponding adjoint problem. A second issue of this paper is the regularization approach. The sequence of approximated solution is obtained by coupling the nonlinear Landweber iteration with iterated Tikhonov regularization. We show that the parameter-to-solution map satisfies sufficient conditions to prove stability and convergence of approximated solutions for the identification problem. We use a unified discrepancy principle as the stopping criteria. Finally, we apply the developed theory in the inverse identification problem of unknown parameters (perfusion coefficient, metabolic heat source) for the identification of tumor regions by thermography.2013-03-25T19:26:10Z2013-03-25T19:26:10Z2012info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfCEZARO, Adriano de; CEZARO, Fabiana Travessini de. Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation. Arxiv, v. 1, p. 1-19, 2012. Disponível em:<http://arxiv.org/pdf/1210.7348v1.pdf>. Acesso em: 21 mar. 2013.http://repositorio.furg.br/handle/1/3201engCezaro, Adriano deCezaro, Fabiana Travessini deinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da FURG (RI FURG)instname:Universidade Federal do Rio Grande (FURG)instacron:FURG2013-03-25T19:26:10Zoai:repositorio.furg.br:1/3201Repositório InstitucionalPUBhttps://repositorio.furg.br/oai/request || http://200.19.254.174/oai/requestopendoar:2013-03-25T19:26:10Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)false |
dc.title.none.fl_str_mv |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation |
title |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation |
spellingShingle |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation Cezaro, Adriano de Uniqueness Thermophysical parameters and source identification Iterative regularization Parabolic type equation Final time measurements |
title_short |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation |
title_full |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation |
title_fullStr |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation |
title_full_unstemmed |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation |
title_sort |
Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation |
author |
Cezaro, Adriano de |
author_facet |
Cezaro, Adriano de Cezaro, Fabiana Travessini de |
author_role |
author |
author2 |
Cezaro, Fabiana Travessini de |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Cezaro, Adriano de Cezaro, Fabiana Travessini de |
dc.subject.por.fl_str_mv |
Uniqueness Thermophysical parameters and source identification Iterative regularization Parabolic type equation Final time measurements |
topic |
Uniqueness Thermophysical parameters and source identification Iterative regularization Parabolic type equation Final time measurements |
description |
In this contribution we show sufficient conditions for simultaneous unique identification of unknown spacewise coefficients and heat source in a parabolic partial differential equation given additional final time measurements. Our approach is based on density, in suitable spaces, of the corresponding adjoint problem. A second issue of this paper is the regularization approach. The sequence of approximated solution is obtained by coupling the nonlinear Landweber iteration with iterated Tikhonov regularization. We show that the parameter-to-solution map satisfies sufficient conditions to prove stability and convergence of approximated solutions for the identification problem. We use a unified discrepancy principle as the stopping criteria. Finally, we apply the developed theory in the inverse identification problem of unknown parameters (perfusion coefficient, metabolic heat source) for the identification of tumor regions by thermography. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012 2013-03-25T19:26:10Z 2013-03-25T19:26:10Z |
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 |
CEZARO, Adriano de; CEZARO, Fabiana Travessini de. Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation. Arxiv, v. 1, p. 1-19, 2012. Disponível em:<http://arxiv.org/pdf/1210.7348v1.pdf>. Acesso em: 21 mar. 2013. http://repositorio.furg.br/handle/1/3201 |
identifier_str_mv |
CEZARO, Adriano de; CEZARO, Fabiana Travessini de. Uniqueness and regularization for unknown spacewise lower-order coefficient and source for the heat type equation. Arxiv, v. 1, p. 1-19, 2012. Disponível em:<http://arxiv.org/pdf/1210.7348v1.pdf>. Acesso em: 21 mar. 2013. |
url |
http://repositorio.furg.br/handle/1/3201 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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.source.none.fl_str_mv |
reponame:Repositório Institucional da FURG (RI FURG) instname:Universidade Federal do Rio Grande (FURG) instacron:FURG |
instname_str |
Universidade Federal do Rio Grande (FURG) |
instacron_str |
FURG |
institution |
FURG |
reponame_str |
Repositório Institucional da FURG (RI FURG) |
collection |
Repositório Institucional da FURG (RI FURG) |
repository.name.fl_str_mv |
Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG) |
repository.mail.fl_str_mv |
|
_version_ |
1807384391140245504 |