Pullback attractors for reaction-diffusion equations in some unbounded domains with an $H^{-1}$-valued non-autonomous forcing term and without uniqueness of solutions

The existence of a pullback attractor for a reaction-diffusion equations in an unbounded domain containing a non-autonomous forcing term taking values in the space $H^{-1}$, and with a continuous nonlinearity which does not ensure uniqueness of solutions, is proved in this paper. The theory of set-valued non-autonomous dynamical systems is applied to the problem.