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Infinite‐dimensional exponential attractors for fourth‐order nonlinear parabolic equations in unbounded domains
Author(s) -
Efendiev Messoud
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1412
Subject(s) - attractor , mathematics , nonlinear system , exponential function , entropy (arrow of time) , mathematical analysis , exponential growth , order (exchange) , exponential type , physics , finance , quantum mechanics , economics
We study in this article the long‐time behavior of solutions of fourth‐order parabolic equations in bfR 3 . 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.