On extinction and non-extinction of solutions for a $p$-Kirchhoff problem with logarithmic nonlinearity

Abstract

In this work, we we study a class of fast diffusion Kirchhoff-type 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 analyze the criteria for the extinction and non-extinction of these solutions.