# American Institute of Mathematical Sciences

January  2007, 18(1): 53-70. doi: 10.3934/dcds.2007.18.53

## The attractors for weakly damped non-autonomous hyperbolic equations with a new class of external forces

 1 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, China, China

Received  March 2006 Revised  October 2006 Published  February 2007

For weakly damped non-autonomous hyperbolic equations, we introduce a new concept Condition (C*), denote the set of all functions satisfying Condition (C*) by L2 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 non-autonomous hyperbolic equations with this new class of time dependent external forces $g(x,t)\in$ L2 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 $D(A)\times H^1_0$.
Citation: Shan Ma, Chengkui Zhong. The attractors for weakly damped non-autonomous hyperbolic equations with a new class of external forces. Discrete & Continuous Dynamical Systems - A, 2007, 18 (1) : 53-70. doi: 10.3934/dcds.2007.18.53
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