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In this paper we consider the following viscoelastic equation:in a bounded domain, and establish a general decay result which is not necessarily of exponential or polynomial type. This work generalizes and improves earlier results in the literature.

In this paper the nonlinear viscoelastic wave equationassociated 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.

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In this paper, we consider the nonlinear viscoelastic equationwith initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for p > m, we prove that there are solutions with positive initial energy that blow up in finite time.