We study asymptotic properties of evolution partial differential equations posed in unbounded spatial domain in the context of locally uniform spaces. This context allows the use of non-integrable data and carries an inherent non-compactness and non-separability. We establish the existence of a lo- cally compact attractor for non-local parabolic equation and weakly damped semilinear wave equation and provide an upper bound on the Kolmogorov's ε-entropy of these attractors and the attractor of strongly damped wave equation in the subcritical case using the method of trajectories. Finally we also investigate infinite dimensional exponential attractors of nonlinear reaction-diffusion equation in its natural energy setting. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:369539 |
| Date | January 2017 |
| Creators | Slavík, Jakub |
| Contributors | Pražák, Dalibor, Miranville, Alain, Skalák, Zdeněk |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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