Asymptotic Regularity and Exponential Attractors for Nonclassical Diusion Equations With Critical Exponent

In this paper, we consider the dynamical behavior of the nonclassical diffusion equation when nonlinearity is critical for both two cases: the forcing term belongs to H ？1 (？) and L2 (？). For the case the forcing term only belongs to H ？1 (？), based on the asymptotic regularity in Dynamical Systems: An International Journal, 26 (4), (2011), 391–400, we prove the existence of exponential attractors in weak topological space H 1 (？). For the case the forcing term belongs to L2 (？), we prove the asymptotic regularity of the solutions and exponential attractors.