  We consider nonlinear parabolic SPDEs of the form $\partial_t
u=-(-\Delta)^{\alpha/2} u + b(u) +\sigma(u)\dot w$, where$\dot w$ denotes
space-time white noise. The functions $b$ and $\sigma$ are both locally
Lipschitz continuous. Under some suitable conditions on the parameters of these
SPDEs, we show that the second moment of their solutions blow up in finite
time. This complements recent works of Khoshnevisan and his coauthors; see for
instance Foondun and Khoshnevisan (2009), Foondun and Khoshnevisan (to appear,
2012) and Conus, Joseph, and Khoshnevisan, as well as those of Chow (Chow,
2009, and Chow, 2011). Furthermore, upon comparing our stochastic equations
with their deterministic counterparts, we find that our results indicates that
the presence of noise might affect the occurrence of blow-up.
