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arXiv · 0810.3369

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

Tomasz Cieślak·Philippe Laurençot
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Abstract

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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Tomasz Cieślak, Philippe Laurençot. 2008-10-19. Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system. https://arxiv.org/abs/0810.3369

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