Global existence and blow-up of solutions to a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity

Menglan Liao; Zhong Tan

paper

Global existence and blow-up of solutions to a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity

arXiv:2010.01483

Abstract

In this paper, a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity under initial-boundary condition is investigated. Based on potential well method and Hardy-Sobolev inequality, the global existence of solutions is derived when the initial energy $J (u_{0})$ is subcritical( $J (u_{0}) < d$ ), critical( $J (u_{0}) = d$ ) with $d$ being the mountain-pass level. Finite time blow-up results are obtained as well when the initial energy $J (u_{0})$ satisfies specific conditions. Moreover, the upper and lower bounds of the blow-up time are given.

18 pages