论文标题
全球存在和对具有奇异潜力和对数非线性的非Newton过滤方程的解决方案的爆炸
Global existence and blow-up of solutions to a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity
论文作者
论文摘要
在本文中，研究了在初始有限条件下具有奇异潜力和对数非线性的一类非Newton过滤方程。基于潜在的井方法和Hardy-Sobolev的不平等，当初始能源$ J（U_0）$是亚批判性（$ J（U_0）<d $），关键（$ j（u_0）= d $）时，解决方案的全球存在将得出。当初始能源$ j（u_0）$满足特定条件时，也会获得有限的时间爆破结果。此外，给出了爆炸时间的上限和下限。
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.
