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Abstract: In this paper, we consider the nonlinear viscoelastic equation with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for , we prove that there are solutions with positive initial energy that blow up in finite time. [Copyright &y& Elsevier]

In this paper we consider the nonlinearly damped semilinear Petrovsky equationutt + Δ2u + aut&z.sfnc;ut&z.sfnc;m − 2 = bu&z.sfnc;u&z.sfnc;p − 2in a bounded domain, where a, b > 0. We prove the existence of a local weak solution and show that this solution blows up in finite time if p > m and the energy is negative. We also show that the solution is global if m ≥ p. [Copyright &y& Elsevier]