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 ) , for large enough l > 0 , then this equation has a strong global attractor in H 0 1 ( Ω ) × L 2 ( Ω ) . We also show that this attractor is a bounded subset of H 2 ( Ω ) ∩ H 0 1 ( Ω ) × H 0 1 ( Ω ) .