We introduce a new method (or technique), asymptotic contractive method, to verify uniform asymptotic compactness of a family of processes. After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearityfsatisfies the polynomial growth of arbitrary order and the time-dependent forcing termgis only translation-bounded inLloc2(R;L2(Ω)).
In this paper, we prove the existence and regularity of pullback attractors for non-autonomous nonclassical diffusion equations with nonlocal diffusion when the nonlinear term satisfies critical exponential growth and the external force term
$h \in L_{l o c}^{2}(\mathbb {R} ; H^{-1}(\Omega )).$
Under some appropriate assumptions, we establish the existence and uniqueness of the weak solution in the time-dependent space
$\mathcal {H}_{t}(\Omega )$
and the existence and regularity of the pullback attractors.