Long-Time Dynamics of the Wave Equation with Nonlocal Weak Damping and Super-Cubic Nonlinearity in 3-D Domains, Part II: Nonautonomous Case

In this paper, we study the long-time dynamics for the nonautonomous wave equation with nonlocal weak damping and super-cubic nonlinearity in a bounded smooth domain of R3.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3.$$\end{document} Based on the Strichartz estimates for the case of bounded domains, we first prove the global well-posedness of the Shatah–Struwe solutions. Then we establish the the concept of uniform φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}-attractor and verify that the family of Shatah–Struwe solution processes has a uniform polynomial attractor, which is a compact uniformly attracting set and attracts any bounded subsets at a polynomial speed.