Global nonexistence for a semilinear Petrovsky equation

In this paper we consider a semilinear Petrovsky equation with damping and source terms. It is proved that the solution blows up in finite time if the positive initial energy satisfies a suitable condition. Moreover for the linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. This is an important breakthrough, since it is only well known that the solution blows up in finite time if the initial energy is negative from all the previous literature.