Taxas ótimas para o decaimento de semigrupos em espaços de Hilbert

• Ano de defesa: 2020
• Autor(a) principal: Genilson Soares de Santana
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE MATEMÁTICA; Programa de Pós-Graduação em Matemática; UFMG
• Palavras-chave em Português: Comportamento assintótico de C0-semigrupos; Taxas ótimas de decaimento; Crescimento positivo; Matemática – Teses; Comportamento assintótico – Teses; Semigrupos de operadores – Teses; Hilbert, Espaços de – Teses
• Link de acesso: http://hdl.handle.net/1843/40105

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.