This paper deals with a class of fast diffusion p-Laplace equation with logarithmic non-linearity in a bounded smooth domain with homogeneous Dirichlet boundary condition. By using energy estimates and some ordinary differential inequalities, we study the conditions on extinction and non-extinction of global solutions. The results of this paper extend and complete the previous studies on this equation.

中文翻译：

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具有对数非线性的快速扩散p -Laplace方程解的灭和不灭

本文研究一类具有齐次Dirichlet边界条件的有界光滑域中具有对数非线性的快速扩散p -Laplace方程。通过使用能量估计和一些常微分不等式，我们研究了整体解灭绝和不灭绝的条件。本文的结果扩展并完成了对该方程的先前研究。