Blow up and global existence in a nonlinear viscoelastic wave equation

In this paper the nonlinear viscoelastic wave equation associated with initial and Dirichlet boundary conditions is considered. Under suitable conditions on g , it is proved that any weak solution with negative initial energy blows up in finite time if p > m . Also the case of a stronger damping is considered and it is showed that solutions exist globally for any initial data, in the appropriate space, provided that m ≥ p .