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Infinite‐dimensional exponential attractors for fourth‐order nonlinear parabolic equations in unbounded domains
Authors:Messoud Efendiev
Institution:Helmholtz Center Munich, Institute of Biomathematics and Biometry, 85764 Neuherberg, Germany
Abstract:We study in this article the long‐time behavior of solutions of fourth‐order parabolic equations in bfR3. In particular, we prove that under appropriate assumptions on the nonlinear interaction function and on the external forces, these equations possess infinite‐dimensional exponential attractors whose Kolmogorov's ε‐entropy satisfies an estimate of the same type as that obtained previously for the ε‐entropy of the global attractor. Copyright © 2011 John Wiley & Sons, Ltd.
Keywords:extended Fisher–  Kolmogorov and Swift–  Hohenberg equations  unbounded domains  global attractor  exponential attractors  kolmogorov's entropy
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