A New Blow-Up Criterion to a Singular Non-Newton Polytropic Filtration Equation

Abstract

In this paper, a singular non-Newton polytropic filtration equation under the initial-boundary value condition is revisited. The finite time blow-up results were discussed when the initial energy E(u0) was subcritical (E(u0)d), critical (E(u0)=d), and supercritical (E(u0)>d), with d being the potential depth by using the potential well method and some differential inequalities. The goal of this paper is to give a finite time blow-up result if E(u0) is independent of d. Moreover, the explicit upper bound of the blow-up time is obtained by the classical Levine’s concavity method, and the precise lower bound of the blow-up time is derived by applying an interpolation inequality.

Keywords

• non-Newton polytropic filtration equation
• blow-up
• the upper and lower bounds of the blow-up time