Global existence and blow-up of weak solutions for a pseudo-parabolic equation with high initial energy

Abstract

This paper deals with a pseudo-parabolic equation involving variable exponents under initial and Dirichlet boundary value conditions. We obtain the global existence and blow-up results of weak solutions with arbitrarily high initial energy. These results extend and improve some recent results in which the blow-up results were showed when the initial energy is nonpositive or positive with a smaller positive upper bound.