Existence and regularity of pullback attractors for a non-autonomous diffusion equation with delay and nonlocal diffusion in time-dependent spaces

In this paper, we study the asymptotic behavior of solution to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space $C_{{\mathcal{H}}_t(\mathrm{\Omega })}$. When the nonlinear function $f$ satisfies the polynomial growth of arbitrary order $p-1$ $(p\ge 2)$ and the external force $h\in L_{loc}^2(\mathbb{R};H^{-1}(\mathrm{\Omega }))$, we establish the existence and regularity of the time-dependent pullback attractors.