JournalsaihpcVol. 27, No. 1pp. 437–446

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

  • Tomasz Cieślak

    Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

  • Philippe Laurençot

    Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France
Finite time blow-up for a one-dimensional quasilinear parabolic–parabolic chemotaxis system cover
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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.

Cite this article

Tomasz Cieślak, Philippe Laurençot, Finite time blow-up for a one-dimensional quasilinear parabolic–parabolic chemotaxis system. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 1, pp. 437–446

DOI 10.1016/J.ANIHPC.2009.11.016