Global existence and blow-up of solutions to a singular Non-Newton polytropic filtration equation with critical and supercritical initial energy

In this paper, we revisit the singular Non-Newton polytropic filtration equation, which was studied extensively in the recent years. However, all the studies are mostly concerned with subcritical initial energy, i.e., \begin{document} $E(u_0) , where \begin{document} $E(u_0)$ \end{document} is the initial energy and \begin{document} $d$ \end{document} is the mountain-pass level. The main purpose of this paper is to study the behaviors of the solution with \begin{document} $E(u_0)≥d$ \end{document} by potential well method and some differential inequality techniques.

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