Upper semicontinuity of pullback D-attractors for nonlinear parabolic equation with nonstandard growth condition

This paper is devoted to the well-posed problem and the existence of pullback D attractors for a class of nonlinear parabolic equation with nonstandard growth condition. First, by making use of Galerkin's method and monotone operator method, the existence of solutions is proved in Orlicz-Sobolev space with variable exponents depending on time and space, then the uniqueness and continuity of solutions are also obtained. Finally, by verifying the pullback D-asymptotic compactness, the existence of pullback D-attractors is proved. In particular, the upper semicontinuity of pullback D-attractors of the corresponding equation with respect to the disturbance parameter ? is also proved.