  Finite time blow-up is shown to occur for solutions to a one-dimensional
quasilinear parabolic-parabolic chemotaxis system as soon as the mean value of
the initial condition exceeds some threshold value. The proof combines a novel
identity of virial type with the boundedness from below of the Liapunov
functional associated to the system, the latter being peculiar to the
one-dimensional setting.

Analysis of PDEs