DD-pullback attractor for a non-autonomous wave equation with additive noise on unbounded domains

This paper is devoted to investigating the asymptotic behavior of solutions of the wave equation with additive noise as well as a non-autonomous term defined on unbounded domains. Firstly, by uniform estimates, a closed DD-pullback absorbing set of dynamical system φφ produced by the mentioned wave equation is obtained. Secondly, the asymptotical compactness of φφ is established by the splitting technique. Finally, the existence of aDD-pullback attractor for corresponding dynamical system φφ in H1(R3)×L2(R3)H1(R3)×L2(R3) is proved, where n≥3n≥3. Particularly, we can show that the DD-pullback attractor is also periodic when the forcing term is periodic.