Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity

In this paper, using a new method (or technique) called “Asymptotic Contractive Semigroup Method” (see Theorem 2.3) we prove the existence of global attractor for the nonclassical diffusion equations in H1(Rn). The nonlinearity satisfies the arbitrary order polynomial growth conditions and the forcing term g only belongs to H−1(Rn). The results obtained essentially improve and complement in some previously published papers.