Global existence and extinction for a fast diffusion p-Laplace equation with logarithmic nonlinearity and special medium void

Abstract

This article is devoted to the global existence and extinction behavior of the weak solution to a fast diffusion pp-Laplace equation with logarithmic nonlinearity and special medium void. By applying energy estimates approach, Hardy-Littlewood-Sobolev inequality, and some ordinary differential inequalities, the global existence result is proved and the sufficient conditions on the occurrence of the extinction and nonextinction phenomena are given.

Keywords

• fast diffusion p-laplace equation
• global existence
• extinction
• nonextinction
• logarithmic nonlinearity
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