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Dimension estimate for the global attractor of an evolution equation. (English) Zbl 1234.35039

Summary: We estimate the dimension of the global attractor of an evolution equation by the study of the evolution of the \(n\)-dimensional volumes under the flow. We compare these results with the estimate of the dimension of the inertial manifold.

MSC:

35B41 Attractors
35B40 Asymptotic behavior of solutions to PDEs
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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