Abstract
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
(
u
0
,
u
1
)
satisfies
∫
R
N
u
0
u
1
d
x
≥
0
. Applications on various models are investigated also.