Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces

Detalhes bibliográficos
Autor(a) principal: Gambera, Laura Rezzieri
Data de Publicação: 2020
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://hdl.handle.net/11449/192683
Resumo: This work presents some results of the theory of the (a,k)-regularized resolvent families, that are the main tool used in this thesis. Related with this families, one result proved in this work is the zero-one law, providing new insights on the structural properties of the theory of (a,k)-regularized resolvent families including strongly continuous semigroups, strongly continuous cosine families, integrated semigroups, among others. Moreover, an abstract nonlinear degenerate hyperbolic equation is considered, that includes the semilinear Blackstock-Crighton-Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, it is proved an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. In addition, under nonlocal initial conditions, a mild solution of the nonlinear equation is established.
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spelling Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spacesLei zero-um para famílias resolvente (a,k)-regularizadas e a equação de Blackstock-Crighton-Westervelt em espaços de Banach(a,k)-regularized resolvent familiesZero-one lawBlackstock-Crighton-Westervelt equationWell-posednessLey cero-unoEquación de Blackstock-Crighton-WesterveltBuen planteamientoFamílias resolvente (a,k)-regularizadasLei zero-umEquação de Blackstock-Crighton-WesterveltBoa colocaçãoThis work presents some results of the theory of the (a,k)-regularized resolvent families, that are the main tool used in this thesis. Related with this families, one result proved in this work is the zero-one law, providing new insights on the structural properties of the theory of (a,k)-regularized resolvent families including strongly continuous semigroups, strongly continuous cosine families, integrated semigroups, among others. Moreover, an abstract nonlinear degenerate hyperbolic equation is considered, that includes the semilinear Blackstock-Crighton-Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, it is proved an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. In addition, under nonlocal initial conditions, a mild solution of the nonlinear equation is established.Este trabajo presenta algunos resultados de la teoría de las familias resolventes (a,k)-regularizadas, que es la principal herramienta utilizada en esta tesis. Relacionado con estas familias, uno de los resultados demostrados en este trabajo es la ley cero-uno, proveyendo nuevas percepciones de propiedades estructurales de la teoría de las familias resolventes (a,k)-regularizdas, incluyendo los semigrupos fuertemente continuos, las familias coseno fuertemente continuas, los semigrupos integrados, entre otras. Además, una ecuación degenerada no lineal abstracta es considerada, la cual incluye la ecuación semilineal de Blackstock-Crighton-Westervelt. Proponiendo un nuevo enfoque basado en semigrupos fuertemente continuos y familias resolvente, es demostrada una representación explícita de las soluciones fuerte y débil de la linealización del modelo por una especie de método de variación de parámetros. Por fin, bajo condiciones iniciales no locales, una solucion débil de la ecuación no lineal es establecida.Este trabalho apresenta alguns resultados da teoria de famílias resolventes (a,k)- regularizadas, que é a principal ferramenta utilizada nesta tese. Relacionado com estas famílias, um resultado provado neste trabalho é a lei zero-um, que fornece novas percepções de propriedades estruturais da teoria de famílias resolventes (a,k)- regularizadas, incluindo os semigrupos fortemente contínuos, as famílias cosseno fortemente contínuas, os semigrupos integrados, entre outras. Além disso, uma equação hiperbólica degenerada não-linear abstrata é considerada, a qual inclui a equação semilinear de Blackstock-Crighton-Westervelt. Propondo uma nova abordagem baseada em semigrupos fortemente contínuos e famílias resolvente, é demonstrada uma representação explícita das soluções forte e branda para a linearização do modelo por uma espécie de método de variação dos parâmetros. Por fim, sob condições iniciais não-locais, uma solução branda da equação não-linear é estabelecida.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES: 001Universidade Estadual Paulista (Unesp)Arita, Andréa Cristina Prokopczyk [UNESP]Lizama, CarlosUniversidade Estadual Paulista (Unesp)Gambera, Laura Rezzieri2020-06-01T13:37:26Z2020-06-01T13:37:26Z2020-04-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfhttp://hdl.handle.net/11449/19268300093155033004153071P0enginfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESP2023-12-25T06:21:44Zoai:repositorio.unesp.br:11449/192683Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:16:17.389203Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
Lei zero-um para famílias resolvente (a,k)-regularizadas e a equação de Blackstock-Crighton-Westervelt em espaços de Banach
title Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
spellingShingle Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
Gambera, Laura Rezzieri
(a,k)-regularized resolvent families
Zero-one law
Blackstock-Crighton-Westervelt equation
Well-posedness
Ley cero-uno
Equación de Blackstock-Crighton-Westervelt
Buen planteamiento
Famílias resolvente (a,k)-regularizadas
Lei zero-um
Equação de Blackstock-Crighton-Westervelt
Boa colocação
title_short Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
title_full Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
title_fullStr Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
title_full_unstemmed Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
title_sort Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces
author Gambera, Laura Rezzieri
author_facet Gambera, Laura Rezzieri
author_role author
dc.contributor.none.fl_str_mv Arita, Andréa Cristina Prokopczyk [UNESP]
Lizama, Carlos
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Gambera, Laura Rezzieri
dc.subject.por.fl_str_mv (a,k)-regularized resolvent families
Zero-one law
Blackstock-Crighton-Westervelt equation
Well-posedness
Ley cero-uno
Equación de Blackstock-Crighton-Westervelt
Buen planteamiento
Famílias resolvente (a,k)-regularizadas
Lei zero-um
Equação de Blackstock-Crighton-Westervelt
Boa colocação
topic (a,k)-regularized resolvent families
Zero-one law
Blackstock-Crighton-Westervelt equation
Well-posedness
Ley cero-uno
Equación de Blackstock-Crighton-Westervelt
Buen planteamiento
Famílias resolvente (a,k)-regularizadas
Lei zero-um
Equação de Blackstock-Crighton-Westervelt
Boa colocação
description This work presents some results of the theory of the (a,k)-regularized resolvent families, that are the main tool used in this thesis. Related with this families, one result proved in this work is the zero-one law, providing new insights on the structural properties of the theory of (a,k)-regularized resolvent families including strongly continuous semigroups, strongly continuous cosine families, integrated semigroups, among others. Moreover, an abstract nonlinear degenerate hyperbolic equation is considered, that includes the semilinear Blackstock-Crighton-Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, it is proved an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. In addition, under nonlocal initial conditions, a mild solution of the nonlinear equation is established.
publishDate 2020
dc.date.none.fl_str_mv 2020-06-01T13:37:26Z
2020-06-01T13:37:26Z
2020-04-17
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.uri.fl_str_mv http://hdl.handle.net/11449/192683
000931550
33004153071P0
url http://hdl.handle.net/11449/192683
identifier_str_mv 000931550
33004153071P0
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.publisher.none.fl_str_mv Universidade Estadual Paulista (Unesp)
publisher.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.source.none.fl_str_mv reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129302638624768

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