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| Author(s): |
Thales Maier de Souza
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2017-01-13 |
| Examining board members: |
Ma To Fu;
Everaldo de Mello Bonotto;
Cícero Lopes Frota;
Gabriela Del Valle Planas
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| Advisor: | Ma To Fu |
| Abstract | |
This thesis is concerned with the study of a class of wave equations with acoustic boundary conditions. We investigate the long-time dynamics of such equations in the case where the system is subject to a non-autonomous external force. In this situation, by adding a weak dissipation, we prove that the problem generates a dissipative evolution process. Our goal is then the existence of non-autonomous attractors. In this direction, we first establishes the existence of a minimal pullback attractor within a universe of tempered sets. We also studied the upper semi-continuity of attractors when the non-autonomous perturbation tends to zero. Our result allows to consider unbounded external forces and nonlinear perturbation with critical (Sobolev) growth. Secondly, we establish the existence of uniform attractors, as well. In view of recent results Zelik (2015) we consider more general external forces than the so called class of translation-compact forces. Part of this thesis was accepted for publication in the journal \\Differential and Integral Equations\" under the title \\Pullback dynamics of non-autonomous wave equations with acoustic boundary condition\". (AU) | |
| FAPESP's process: | 13/04648-5 - Non-autonomous equations in hyperbolic thermoelasticity |
| Grantee: | Thales Maier de Souza |
| Support Opportunities: | Scholarships in Brazil - Doctorate |