In this paper, we investigate the existence of pullback attractors for a nonclassical diffusion equation with Dirichlet boundary condition in $ H^2(\Omega)\cap H^1_0(\Omega) $. First, we prove the existence and uniqueness of strong solutions for a nonclassical diffusion equation. Then we prove the existence of pullback attractors in $ H^2(\Omega)\cap H^1_0(\Omega) $ by applying asymptotic a priori estimate method.
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