PULLBACK ATTRACTORS FOR REACTION-DIFFUSION EQUATIONS IN SOME UNBOUNDED DOMAINS WITH AN H~(-1)-VALUED NON-AUTONOMOUS FORCING TERM AND WITHOUT UNIQUENESS OF SOLUTIONS

摘要

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.