Pullback dynamics of nonautonomous supercritical wave equations on compact Riemannian manifolds
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...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Brasil |
| Institución: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-31082020-092702 |
| Acceso en línea: | https://www.teses.usp.br/teses/disponiveis/55/55135/tde-31082020-092702/ |
| Access Level: | acceso abierto |
| Palabra clave: | Atrator exponencial pullback Continuidade de atratores Continuity of attractors Equação da onda supercrítica Pullback exponential attractor Supercritical wave equation |
| Sumario: | 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. |
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