Strong Global Attractors for 3D Wave Equations with Weakly Damping

Abstract

We consider the existence of the global attractor A1 for the 3D weakly damped wave equation. We prove that A1 is compact in (H2(Ω)∩H01(Ω))×H01(Ω) and attracts all bounded subsets of (H2(Ω)∩H01(Ω))×H01(Ω) with respect to the norm of (H2(Ω)∩H01(Ω))×H01(Ω). Furthermore, this attractor coincides with the global attractor in the weak energy space H01(Ω)×L2(Ω).