Pullback DD-attractors for nonautonomous sine–Gordon equations

In this paper, we consider the pullback DD-attractor for the nonautonomous sine–Gordon wave equation. We will show the existence of the pullback DD-attractor in V×HV×H and in D(A)×VD(A)×V. To this end, some abstract results are established. We use the methods provided by Q.F. Ma, S.H. Wang, C.K. Zhong, Necessary and sufficient conditions for the existence of global attractors for semigroups and applications, J. Indiana Univ. Math. 51 (6) (2002), to establish some sufficient conditions for the existence of the pullback DD-attractor of an infinite dimensional dynamical system.