GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A SINGULAR NON-NEWTON POLYTROPIC FILTRATION EQUATION WITH CRITICAL AND SUPERCRITICAL INITIAL ENERGY

摘要

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., E(u(0)) d, where E(u(0)) is the initial energy and d is the mountain-pass level. The main purpose of this paper is to study the behaviors of the solution with E(u(0)) = d by potential well method and some differential inequality techniques.