Blow-up of solutions to p(x)-Laplacian parabolic equations with general nonlinear source

Abstract

In this paper, we study a p(x)-Laplacian parabolic equation with a general nonlinear source term. We show that the solution may blow up in finite time at positive initial energy. Moreover, under some suitable assumptions about the nonlinear source term, we prove that solutions blow up in finite time at arbitrarily high initial energy.