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

• Ano de defesa: 2020
• Autor(a) principal: Gambera, Laura Rezzieri
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: (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
• Link de acesso: http://hdl.handle.net/11449/192683

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.