Pullback dynamics of nonautonomous supercritical wave equations on compact Riemannian manifolds

• Ano de defesa: 2020
• Autor(a) principal: Tavares, Eduardo Henrique Gomes
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Atrator exponencial pullback; Continuidade de atratores; Continuity of attractors; Equação da onda supercrítica; Pullback exponential attractor; Supercritical wave equation
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-31082020-092702/

This thesis is concerned with large-time dynamics of non-autonomous wave equations defined on compact Riemannian manifolds with boundary. It contains three main contributions. First, we give a detailed proof of well-posedness for the wave equation with supercritical nonlinearities and time-dependent external forces, on the energy space. It is a slight generalization of known results for autonomous problems. However our arguments are different. Thus, the wave problem can be studied as a non-autonomous dynamical system since its finite energy solution flows define a continuous evolution process. Next, we establish the existence of pullback exponential attractors to this non-autonomous system, such that any section have finite fractal dimensions on the natural energy space. Finally, in the case of external force is dependent on a parameter, we study the continuity of pullback attractors with respect to it.