Global Existence and Nonexistence in a System of Petrovsky

In this paper we consider the nonlinearly damped semilinear Petrovsky equation utt + 2u + aut ut m−2 = bu u p−2 in a bounded domain, where a b > 0.W e 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.W e also show that the solution is global if m ≥ p.