Geodesic
Finite time blow-up for a one-dimensional quasilinear parabolic–parabolic chemotaxis system
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 437-446

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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.

@article{AIHPC_2010__27_1_437_0,
     author = {Cie\'slak, Tomasz and Lauren\c{c}ot, Philippe},
     title = {Finite time blow-up for a one-dimensional quasilinear parabolic{\textendash}parabolic chemotaxis system},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {437--446},
     publisher = {Elsevier},
     volume = {27},
     number = {1},
     year = {2010},
     doi = {10.1016/j.anihpc.2009.11.016},
     mrnumber = {2580517},
     zbl = {1270.35377},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2009.11.016/}
}
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Cieślak, Tomasz; Laurençot, Philippe. Finite time blow-up for a one-dimensional quasilinear parabolic–parabolic chemotaxis system. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 437-446. doi: 10.1016/j.anihpc.2009.11.016

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