English

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

Analysis of PDEs 2008-10-21 v1

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.

Keywords

Cite

@article{arxiv.0810.3369,
  title  = {Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system},
  author = {Tomasz Cieślak and Philippe Laurençot},
  journal= {arXiv preprint arXiv:0810.3369},
  year   = {2008}
}