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Let Ω ⊂ R N , N ≤ 3, be a bounded domain with smooth boundary, γ ∈ L 2 (Ω) be arbitrary and φ : R → R be a C 1 -function satisfying a subcritical growth condition. For every ε ∈ ]0, ∞[ consider the semiflow π ε on H 1 0 (Ω) × L 2 (Ω) generated by the damped wave equation 2000 Mathematics Subject Classification: Primary 37B30, 35B25; Secondary 37L05, 37L65.doi:10.4064/fm196-3-3 fatcat:sd724jmjczhz5bdb2m44k72l5i