In this paper, we study a class of fast diffusion p-Laplace equation with singular potential in a bounded smooth domain with homogeneous Dirichlet boundary condition. By using energy estimates, Hardy-Littlewood-Sobolev inequality, and some ordinary differential inequalities, we get the solution of the equation exists globally. Moreover, the conditions of extinction and non-extinction are studied. The results of this paper extend and complete the previous studies on this equation.

中文翻译：

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具有奇异势的快速扩散p-Laplace发展方程解的整体存在，灭绝和不灭绝

在本文中，我们研究了在齐次Dirichlet边界条件的有界光滑域中具有奇异势的一类快速扩散p -Laplace方程。通过使用能量估计，Hardy-Littlewood-Sobolev不等式和一些常微分不等式，我们得到方程的解存在全局。此外，还研究了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。