A strong global attractor for the 3D wave equation with displacement dependent damping

We prove that if the displacement coefficient of the damping of the 3D wave equation is a positive constant on the interval (−l,l)(−l,l), for large enough l>0l>0, then this equation has a strong global attractor in H01(Ω)×L2(Ω). We also show that this attractor is a bounded subset of H2(Ω)∩H01(Ω)×H01(Ω).