Fu Qi, YINSheng Fa, n ZHOUZi Gen OUYA, NGCui Hui XIAO
Acta Mathematica Sinica. 2009, 25(2): 0-0.
We consider the asymptotic behavior of
solutions of a lattice dynamical system of dissipative Zakharov
equation. By introducing a new weight inner product and norm in
the space and establishing uniform estimate on `` Tail Ends" of
solutions, we successfully overcome some difficulties raised by
the lack of Sobolev compact embedding in the case of unbounded
domains, and prove the existence of the global attractor; then by
using element decomposition and the covering property of a
polyhedron in the finite-dimensional space, we obtain the upper
bound for the Kolmogorov $\epsilon$-entropy of the global
attractor; finally, we consider the upper semicontinuity of the
global attractor.