Abstract
We consider the dynamical behavior of the nonclassical diffusion equation with critical nonlinearity for both autonomous and nonautonomous cases. For the autonomous case, we obtain the existence of a global attractor when the forcing term only belongs to H−1, this result simultaneously resolves a problem in Acta Mathematicae Applicatae Sinica 18 (2002), 273–276 related to the critical exponent. For the nonautonomous case, assumed that the time-dependent forcing term is translation bounded instead of translation compact, we first prove the asymptotic regularity of solutions, then the existence of a compact uniform attractor together with its structure and regularity has been obtained; finally, we show the existence of (nonautonomous) exponential attractors.