A blow-up result for a nonlinear wave equation with damping and vanishing initial energy in RN

In this paper we consider the Cauchy problem for a nonlinear wave equation with linear damping and source terms. It is proved that the solution blows up in finite time even for vanishing initial energy if the initial datum (u0,u1)(u0,u1) satisfies ∫RNu0u1dx≥0. Applications on various models are investigated also.