Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations

We consider the initial-boundary value problem for degenerate parabolic and pseudo-parabolic equations associated with Hörmander-type operator. Under the subcritical growth restrictions on the nonlinearity f(u), which are determined by the generalized Métivier index, we establish the global existence of solutions and the corresponding attractors. Finally, we show the upper semicontinuity of the attractors in the topology of HX,01(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{X,0}^1(\Omega )$$\end{document}.