The attractors for weakly damped nonautonomous hyperbolic equations with a new class of external forces
Shan Ma  School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, China (email) Abstract: For weakly damped nonautonomous hyperbolic equations, we introduce a new concept Condition (C*), denote the set of all functions satisfying Condition (C*) by L^{2} _{C* } $(R;X)$ which are translation bounded but not translation compact in $L^2$ _{loc}$(R;X)$, and show that there are many functions satisfying Condition (C*); then we study the uniform attractors for weakly damped nonautonomous hyperbolic equations with this new class of time dependent external forces $g(x,t)\in $ L^{2} _{C* } $(R;X)$ and prove the existence of the uniform attractors for the family of processes corresponding to the equation in $H^1_0\times L^2$ and $D(A)\times H^1_0$.
Keywords: uniform attractor; translation compact; uniformly ωlimit compact;
uniform Condition (C); Condition (C*); damped hyperbolic equations.
Received: March 2006; Revised: October 2006; Available Online: February 2007. 
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