In this paper, the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.
The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E1 space is obtained.
Abstract In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equationgoverning the modulated wave instabilities in E0 is considered.By a decomposition of solution operator,it isshown that the global attractor in E0 is actually equal to a global attractor in E1.
Zheng-de DaiDepartment of Mathematics, Yunnan University, Kunming 650091, China
