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 solutions to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space CHt(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{\mathcal {H}_{t}(\varOmega )}$$\end{document}. When the nonlinear function f satisfies the polynomial growth of arbitrary order p-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p-1$$\end{document}(p≥2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p \ge 2)$$\end{document} and the external force h∈Lloc2R;H-1(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h \in L_{l o c}^{2}\left( \mathbb {R}; H^{-1}(\varOmega )\right) $$\end{document}, we establish the existence and regularity of the time-dependent pullback attractors.