Global Existence and Nonexistence in a System of Petrovsky

In this paper we consider the nonlinearly damped semilinear Petrovsky equation<f>utt + Δ2u + aut&z.sfnc;ut&z.sfnc;m − 2 = bu&z.sfnc;u&z.sfnc;p − 2</f>in 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]