Klein-Gordon models with non-effective time-dependent potential

Detalhes bibliográficos
Ano de defesa: 2016
Autor(a) principal: Nascimento, Wanderley Nunes do
Orientador(a): Kapp, Rafael Augusto dos Santos lattes
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: eng
Instituição de defesa: Universidade Federal de São Carlos
Câmpus São Carlos
Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Inglês:
Klein-Gordon time-dependent equation
WKB Analysis
Strichartz estimates
Semi-linear wave equation
Power non-linearity
Área do conhecimento CNPq:
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: https://repositorio.ufscar.br/handle/ufscar/7453
Resumo: In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.
id SCAR_ab8a7dbf05fccce4a271ee31749300a9
oai_identifier_str oai:repositorio.ufscar.br:ufscar/7453
network_acronym_str SCAR
network_name_str Repositório Institucional da UFSCAR
repository_id_str
spelling Nascimento, Wanderley Nunes doKapp, Rafael Augusto dos Santoshttp://lattes.cnpq.br/2872257628868649Ebert, Marcelo Rempelhttp://lattes.cnpq.br/2266906291626715http://lattes.cnpq.br/61502635886083892016-09-26T20:35:40Z2016-09-26T20:35:40Z2016-02-19NASCIMENTO, Wanderley Nunes do. Klein-Gordon models with non-effective time-dependent potential. 2016. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7453.https://repositorio.ufscar.br/handle/ufscar/7453In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.Nesta tese estudamos as propriedades assintóticas para a solução do problema de Cauchy para a equação de Klein-Gordon com potencial não efetivo dependente do tempo. O principal objetivo foi definir uma energia adequada relacionada ao problema de Cauchy e derivar estimativas para tal energia. Estimativas de Strichartz e resultados de scatering e scatering modificados também foram estabelecidos. A teoria C m e a condição de estabilização foram aplicados para tratar o caso em que o coeficiente da massa oscila muito rápido. Além disso, consideramos um mod- elo de onda semi-linear scale-invariante com massa e dissipação dependentes do tempo, nesta etapa usamos as estimativas lineares de tal modelo para provar ex- istência global (no tempo) de solução de energia para dados iniciais suficientemente pequenos e demonstramos um resultado de blow-up para uma escolha adequada dos coeficientes.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)engUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarKlein-Gordon time-dependent equationWKB AnalysisStrichartz estimatesSemi-linear wave equationPower non-linearityCIENCIAS EXATAS E DA TERRA::MATEMATICAKlein-Gordon models with non-effective time-dependent potentialinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisOnlineinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTeseWNN.pdfTeseWNN.pdfapplication/pdf1247691https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/1/TeseWNN.pdf63f743255181169a9bb4ca1dfd2312c2MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTTeseWNN.pdf.txtTeseWNN.pdf.txtExtracted texttext/plain331408https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/3/TeseWNN.pdf.txt4ab03b5b7c36329c4d7c4a4411965ddaMD53THUMBNAILTeseWNN.pdf.jpgTeseWNN.pdf.jpgIM Thumbnailimage/jpeg7054https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/4/TeseWNN.pdf.jpg779d100ac759f0ce49ef6162ed78b590MD54ufscar/74532019-09-11 02:16:41.791oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-05-25T12:52:37.734783Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false
dc.title.eng.fl_str_mv Klein-Gordon models with non-effective time-dependent potential
title Klein-Gordon models with non-effective time-dependent potential
spellingShingle Klein-Gordon models with non-effective time-dependent potential
Nascimento, Wanderley Nunes do
Klein-Gordon time-dependent equation
WKB Analysis
Strichartz estimates
Semi-linear wave equation
Power non-linearity
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Klein-Gordon models with non-effective time-dependent potential
title_full Klein-Gordon models with non-effective time-dependent potential
title_fullStr Klein-Gordon models with non-effective time-dependent potential
title_full_unstemmed Klein-Gordon models with non-effective time-dependent potential
title_sort Klein-Gordon models with non-effective time-dependent potential
author Nascimento, Wanderley Nunes do
author_facet Nascimento, Wanderley Nunes do
author_role author
dc.contributor.authorlattes.por.fl_str_mv http://lattes.cnpq.br/6150263588608389
dc.contributor.author.fl_str_mv Nascimento, Wanderley Nunes do
dc.contributor.advisor1.fl_str_mv Kapp, Rafael Augusto dos Santos
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/2872257628868649
dc.contributor.advisor-co1.fl_str_mv Ebert, Marcelo Rempel
dc.contributor.advisor-co1Lattes.fl_str_mv http://lattes.cnpq.br/2266906291626715
contributor_str_mv Kapp, Rafael Augusto dos Santos
Ebert, Marcelo Rempel
dc.subject.eng.fl_str_mv Klein-Gordon time-dependent equation
WKB Analysis
Strichartz estimates
Semi-linear wave equation
Power non-linearity
topic Klein-Gordon time-dependent equation
WKB Analysis
Strichartz estimates
Semi-linear wave equation
Power non-linearity
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.
publishDate 2016
dc.date.accessioned.fl_str_mv 2016-09-26T20:35:40Z
dc.date.available.fl_str_mv 2016-09-26T20:35:40Z
dc.date.issued.fl_str_mv 2016-02-19
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv NASCIMENTO, Wanderley Nunes do. Klein-Gordon models with non-effective time-dependent potential. 2016. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7453.
dc.identifier.uri.fl_str_mv https://repositorio.ufscar.br/handle/ufscar/7453
identifier_str_mv NASCIMENTO, Wanderley Nunes do. Klein-Gordon models with non-effective time-dependent potential. 2016. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7453.
url https://repositorio.ufscar.br/handle/ufscar/7453
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.publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática - PPGM
dc.publisher.initials.fl_str_mv UFSCar
publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFSCAR
instname:Universidade Federal de São Carlos (UFSCAR)
instacron:UFSCAR
instname_str Universidade Federal de São Carlos (UFSCAR)
instacron_str UFSCAR
institution UFSCAR
reponame_str Repositório Institucional da UFSCAR
collection Repositório Institucional da UFSCAR
bitstream.url.fl_str_mv https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/1/TeseWNN.pdf
https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/2/license.txt
https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/3/TeseWNN.pdf.txt
https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7453/4/TeseWNN.pdf.jpg
bitstream.checksum.fl_str_mv 63f743255181169a9bb4ca1dfd2312c2
ae0398b6f8b235e40ad82cba6c50031d
4ab03b5b7c36329c4d7c4a4411965dda
779d100ac759f0ce49ef6162ed78b590
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)
repository.mail.fl_str_mv
_version_ 1767351107675226112

Registros relacionados