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

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

2008-10-19

arxiv.org/abs/0810.3369v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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