The ε-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors
We prove an estimation of the Kolmogorov ε-entropy in H of the unitary ball in the space V, where H is a Hilbert space and V is a Sobolev-like subspace of H. Then, by means of Zelik’s result, an estimate of the fractal dimension of the attractors of some nonlinear parabolic equations is established.
| Authors: | ; |
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| Format: | Article |
| Status: | Submitted version |
| Publication date: | 2017 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/73816 |
| Online Access: | https://hdl.handle.net/11441/73816 https://doi.org/10.3934/eect.2017018 |
| Access Level: | Open access |
| Keyword: | Fractal dimension Attractors Entropy |
| Summary: | We prove an estimation of the Kolmogorov ε-entropy in H of the unitary ball in the space V, where H is a Hilbert space and V is a Sobolev-like subspace of H. Then, by means of Zelik’s result, an estimate of the fractal dimension of the attractors of some nonlinear parabolic equations is established. |
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