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

Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system