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Long time behavior of a damped generalized BBM equation in low regularity spaces
Authors:Ming Wang
Affiliation:School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei, China
Abstract:Long‐time behavior of solutions of a damped, forced generalized Benjamin‐Bona‐Mahony equation with periodic boundary condition is studied. Assume that the force fL2 and the damping coefficient is a small perturbation of a positive constant, the existence of global attractor below H1 is proved. Moreover, we show the global attractor has finite fractal dimension in the sharp regularity space H2. 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 H2. Copyright © 2015 John Wiley & Sons, Ltd.
Keywords:generalized BBM equation  global attractor  fractal dimension  I−  operator
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