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Global Existence, Extinction, and Non-Extinction of Solutions to a Fast Diffusion p -Laplace Evolution Equation with Singular Potential
Journal of Dynamical and Control Systems ( IF 0.6 ) Pub Date : 2019-09-05 , DOI: 10.1007/s10883-019-09462-5
Xiumei Deng , Jun Zhou

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:

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。
更新日期:2019-09-05
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