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Silas Luiz de Carvalhohttp://lattes.cnpq.br/1589518857002416Emerson Alves Mendonça de AbreuMarcos da Silva MontenegroPedro Tavares Paes Lopeshttp://lattes.cnpq.br/3001350332450722Genilson Soares de Santana2022-03-15T17:06:41Z2022-03-15T17:06:41Z2020-02-19http://hdl.handle.net/1843/40105O presente texto consiste em uma apresentação detalhada dos principais resultados em [6], [7], [11] e [36], os quais discutem a relação existente entre o comportamento assintótico de C0-semigrupos em espaços Hilbert e as taxas de crescimento das normas dos operadores resolventesassociados aos respectivos geradores infinitesimais. O principal resultado que apresentamosnos diz que podemos obter taxas ótimas para o decaimento de C0-semigrupos se a norma doresolvente do gerador comportar como uma função de crescimento positivo (que, grosso modo,possui um crescimento mais rápido que o polinomial). Para uma grande classe de semigrupos, esta condição não é apenas suficiente, mas também necessária para que esta estimativa ótimaseja mantida. Apresentamos ainda uma ilustração dos resultados teóricos, usados para obterestimativas precisas sobre a taxa de decaimento da energia para uma equação da onda sujeita aamortecimento viscoelástico na fronteira.The present text consists of a detailed presentation of the main results in [6], [7], [11] and [36], which discuss the existing relation between the asymptotic behavior of C0-semigroups in Hilbert spaces and the growth rates of the resolvent operators norms associated with the respective infinitesimal generators. The main result we present tells us that we can obtain optimal rates for the decay of C0-semigroups if the norm of the resolvent associated with generator behave likepositive increase functions (which, roughly, grow faster at least with a power-law rates). For a large class of semigroups, this condition is not only sufficient, but also necessary for this optimal estimate to be hold. We also present an application of the theoretical results, used to obtain sharp estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorporUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em MatemáticaUFMGBrasilICX - DEPARTAMENTO DE MATEMÁTICAhttp://creativecommons.org/licenses/by-nc-nd/3.0/pt/info:eu-repo/semantics/openAccessMatemática – TesesComportamento assintótico – TesesSemigrupos de operadores – TesesHilbert, Espaços de – TesesComportamento assintótico de C0-semigruposTaxas ótimas de decaimentoCrescimento positivoTaxas ótimas para o decaimento de semigrupos em espaços de Hilbertinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALTaxas ótimas para o decaimento de semigrupos em espaços de Hilbert-Corrigido.pdfTaxas ótimas para o decaimento de semigrupos em espaços de Hilbert-Corrigido.pdfapplication/pdf1389432https://repositorio.ufmg.br/bitstream/1843/40105/4/Taxas%20%c3%b3timas%20para%20o%20decaimento%20de%20semigrupos%20em%20espa%c3%a7os%20de%20Hilbert-Corrigido.pdff0e7ab026a5f36571838b854409b259aMD54CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufmg.br/bitstream/1843/40105/2/license_rdfcfd6801dba008cb6adbd9838b81582abMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/40105/5/license.txtcda590c95a0b51b4d15f60c9642ca272MD551843/401052022-03-15 15:37:54.965oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2022-03-15T18:37:54Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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