A new blow-up criterion for non-Newton filtration equations with special medium void

Abstract

This paper deals with the finite time blow-up of solutions to the initial boundary value problem of a non-Newton filtration equation with special medium void. A new criterion for the solutions to blow up in finite time is established by using the Hardy inequality. Moreover, the upper and lower bounds for the blow-up time are also estimated. The results solve an open problem proposed by Liu in 2016.