Attractors for non-autonomous wave equations with a new class of external forces ✩

We introduce a new concept Condition (C*), and denote the set of all functions satisfying Condition (C*) by L2c ∗(R;X), which are translation bounded but not translation compact in L2 loc(R;X), and we show that there are many functions satisfying Condition (C*); then, in application, we obtain the existence of uniform attractors in E0 = H1 0 ×L2 for non-autonomous wave equations involving mixed differential quotient terms with this new class of time dependent external forces h(x, t) ∈ L2c ∗(R;X). © 2007 Elsevier Inc. All rights reserved.