A complete classification of initial energy in a [formula omitted]-Laplace pseudo-parabolic equation

Abstract

This paper deals with a pseudo-parabolic equation involving p(x)-Laplacian, which has been studied in Di et al. (2017), Zhu et al. (2020) and Liao (2019). By the variational methods and embedding inequalities, we determine the complete classification of blow-up and global existence of weak solutions in some Sobolev space with variable exponent by covering all kinds of initial energy characterized with the mountain pass level.