Global existence, extinction, and non-extinction of solutions to a fast diffusion p-Laplace evolution equation with logarithmic nonlinearity

In this paper, we study a class of fast diffusion p-Laplace equation with logarithmic nonlinearity. Under appropriate conditions, by applying energy estimates in combination with the Galerkin method and Sobolev inequality, we establish the global existence of solutions. Moreover, we obtain the extinction and non-extinction properties of these solutions.