Long time behavior of a damped generalized BBM equation in low regularity spaces | Zendy

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Long time behavior of a damped generalized BBM equation in low regularity spaces

Author(s) -

Wang Ming

Publication year - 2015

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.3400

Subject(s) - attractor , mathematics , mathematical analysis , fractal dimension , fractal , perturbation (astronomy) , dimension (graph theory) , boundary (topology) , constant (computer programming) , space (punctuation) , periodic boundary conditions , boundary value problem , pure mathematics , physics , linguistics , philosophy , quantum mechanics , computer science , programming language

Long‐time behavior of solutions of a damped, forced generalized Benjamin‐Bona‐Mahony equation with periodic boundary condition is studied. Assume that the force f ∈ L 2 and the damping coefficient is a small perturbation of a positive constant, the existence of global attractor below H 1 is proved. Moreover, we show the global attractor has finite fractal dimension in the sharp regularity space H 2 . Finally, we give a covering of the global attractor, which suggests that the attractor is even thinner than a general set with finite fractal dimension in H 2 . Copyright © 2015 John Wiley & Sons, Ltd.

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