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Attractors and Approximate Inertial Manifolds for the Generalized Benjamin–Bona–Mahony Equation
Author(s) -
Wang Bixiang
Publication year - 1997
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/(sici)1099-1476(199702)20:3<189::aid-mma852>3.0.co;2-e
Subject(s) - mathematics , attractor , hausdorff space , inertial frame of reference , fractal , a priori and a posteriori , integer (computer science) , mathematical analysis , a priori estimate , cahn–hilliard equation , pure mathematics , partial differential equation , classical mechanics , philosophy , physics , epistemology , computer science , programming language
In the present paper, we deal with the long time behaviour of solutions for the generalized Benjamin–Bona–Mahony equation. By a priori estimates methods, we show this equation possesses a global attractor in H k for every integer k ⩾2, which has finite Hausdorff and fractal dimensions. We also construct approximate inertial manifolds such that every solution enters their thin neighbourhood in a finite time. © 1997 by B.G. Teubner Stuttgart‐John Wiley & Sons, Ltd.