  We are concerned with nonexistence results for a class of quasilinear
parabolic differential problems with a potential in $\Omega\times(0,+\infty)$,
where $\Omega$ is a bounded domain. In particular, we investigate how the
behavior of the potential near the boundary of the domain and the power
nonlinearity affect the nonexistence of solutions. Particular attention is
devoted to the special case of the semilinear parabolic problem, for which we
show that the critical rate of growth of the potential near the boundary
ensuring nonexistence is sharp.
