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

TL;DR

This paper studies the conditions under which solutions to a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity exist globally or blow up in finite time, using potential well and Hardy-Sobolev methods.

Contribution

It establishes new criteria for global existence and blow-up of solutions based on initial energy levels, extending understanding of such nonlinear filtration equations.

Findings

Global solutions exist when initial energy is subcritical or critical.

Finite time blow-up occurs under certain initial energy conditions.

Bounds for blow-up time are explicitly derived.

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.