Singular Solutions in a p(x)-Laplace Equation with Multi-sources.

This paper deals with a p(x)-Laplacian parabolic problem involving positive and negative sources, subject to a homogeneous Dirichlet boundary condition. We classify the initial energy and the Nehari energy completely to show global existence and blow-up of weak solutions. More- over, we obtain non-extinction and extinction properties of weak solutions. [ABSTRACT FROM AUTHOR]