Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications

Detalhes bibliográficos
Autor(a) principal: Santana, Marcos Gabriel de
Data de Publicação: 2021
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFS
Texto Completo: http://ri.ufs.br/jspui/handle/riufs/16245
Resumo: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
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spelling Santana, Marcos Gabriel deSantos, Bruno Luis de Andrade2022-09-02T15:24:18Z2022-09-02T15:24:18Z2021-02-26SANTANA, Marcos Gabriel de. Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications. 2021. 107 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2021.http://ri.ufs.br/jspui/handle/riufs/16245Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão CristóvãoIn this work, we study the initial value problem associated with the abstract integrodifferential equation u'(t) = S g(t − s)Au(s)ds + f(t, u(t)), t > 0, with critical or subcritical nonlinearity f in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and blow-up alternative of the E-regular solution that satisfies a specific condition of controlled behavior at t = 0. Then, we apply the theory to the Navier-Stokes problem with hereditary viscosity and initial data in the scale of fractional power spaces associated with the Stokes operator; and to reaction-diffusion problems with super-linear and gradient nonlinearities, and initial data in Lebesgue and Besov spaces, respectively.engMatemáticaEquações diferenciais não-linearesEquações de Navier-StokesIntegrodifferential equationsCritical nonlinearitiesLocal well-posednessContinuation and blow-up alternativeRegularity theoryNavier-Stokes with hereditary viscosityReaction-diffusion with memoryCIENCIAS EXATAS E DA TERRA::MATEMATICAWell-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applicationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisPós-Graduação em MatemáticaUniversidade Federal de Sergipereponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/16245/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALMARCOS_GABRIEL_SANTANA.pdfMARCOS_GABRIEL_SANTANA.pdfapplication/pdf1373148https://ri.ufs.br/jspui/bitstream/riufs/16245/2/MARCOS_GABRIEL_SANTANA.pdf5f1ee51617db61f47aed03eee90ff0e7MD52TEXTMARCOS_GABRIEL_SANTANA.pdf.txtMARCOS_GABRIEL_SANTANA.pdf.txtExtracted texttext/plain184456https://ri.ufs.br/jspui/bitstream/riufs/16245/3/MARCOS_GABRIEL_SANTANA.pdf.txted5e6accc8495613071517409e173351MD53THUMBNAILMARCOS_GABRIEL_SANTANA.pdf.jpgMARCOS_GABRIEL_SANTANA.pdf.jpgGenerated Thumbnailimage/jpeg1410https://ri.ufs.br/jspui/bitstream/riufs/16245/4/MARCOS_GABRIEL_SANTANA.pdf.jpg484d39d264601ca27beb6094628e7256MD54riufs/162452022-09-02 12:24:25.418oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2022-09-02T15:24:25Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
title Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
spellingShingle Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
Santana, Marcos Gabriel de
Matemática
Equações diferenciais não-lineares
Equações de Navier-Stokes
Integrodifferential equations
Critical nonlinearities
Local well-posedness
Continuation and blow-up alternative
Regularity theory
Navier-Stokes with hereditary viscosity
Reaction-diffusion with memory
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
title_full Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
title_fullStr Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
title_full_unstemmed Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
title_sort Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
author Santana, Marcos Gabriel de
author_facet Santana, Marcos Gabriel de
author_role author
dc.contributor.author.fl_str_mv Santana, Marcos Gabriel de
dc.contributor.advisor1.fl_str_mv Santos, Bruno Luis de Andrade
contributor_str_mv Santos, Bruno Luis de Andrade
dc.subject.por.fl_str_mv Matemática
Equações diferenciais não-lineares
Equações de Navier-Stokes
topic Matemática
Equações diferenciais não-lineares
Equações de Navier-Stokes
Integrodifferential equations
Critical nonlinearities
Local well-posedness
Continuation and blow-up alternative
Regularity theory
Navier-Stokes with hereditary viscosity
Reaction-diffusion with memory
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Integrodifferential equations
Critical nonlinearities
Local well-posedness
Continuation and blow-up alternative
Regularity theory
Navier-Stokes with hereditary viscosity
Reaction-diffusion with memory
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
publishDate 2021
dc.date.issued.fl_str_mv 2021-02-26
dc.date.accessioned.fl_str_mv 2022-09-02T15:24:18Z
dc.date.available.fl_str_mv 2022-09-02T15:24:18Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv SANTANA, Marcos Gabriel de. Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications. 2021. 107 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2021.
dc.identifier.uri.fl_str_mv http://ri.ufs.br/jspui/handle/riufs/16245
identifier_str_mv SANTANA, Marcos Gabriel de. Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications. 2021. 107 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2021.
url http://ri.ufs.br/jspui/handle/riufs/16245
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.program.fl_str_mv Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv Universidade Federal de Sergipe
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFS
instname:Universidade Federal de Sergipe (UFS)
instacron:UFS
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instacron_str UFS
institution UFS
reponame_str Repositório Institucional da UFS
collection Repositório Institucional da UFS
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