A blow-up mechanism for a chemotaxis model

Miguel A. Herrero; Juan J. L. Velazquez

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 24, Issue: 4, page 633-683
  • ISSN: 0391-173X

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Herrero, Miguel A., and Velazquez, Juan J. L.. "A blow-up mechanism for a chemotaxis model." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24.4 (1997): 633-683. <http://eudml.org/doc/84273>.

@article{Herrero1997,
author = {Herrero, Miguel A., Velazquez, Juan J. L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {homogeneous Neumann conditions; Dirac-delta type singularity in finite time; inner layer around the unfolding singularity},
language = {eng},
number = {4},
pages = {633-683},
publisher = {Scuola normale superiore},
title = {A blow-up mechanism for a chemotaxis model},
url = {http://eudml.org/doc/84273},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Herrero, Miguel A.
AU - Velazquez, Juan J. L.
TI - A blow-up mechanism for a chemotaxis model
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 24
IS - 4
SP - 633
EP - 683
LA - eng
KW - homogeneous Neumann conditions; Dirac-delta type singularity in finite time; inner layer around the unfolding singularity
UR - http://eudml.org/doc/84273
ER -

References

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  1. [E] S.D. Eidelman, Parabolic systems, North-Holland, Amsterdam, 1969. Zbl0181.37403MR252806
  2. [FL] R.M. Ford - D.A. Lauffenburger, Analysis of chemotactical bacterial distribution in population migration assays using a mathematical model applicable to steep or shallow attractant gradients, Bull. Math. Biol.53 (1991), 721-749. Zbl0729.92029
  3. [KS] E.F. Keller - L.A. Segel, Initiation ofslime mold aggregation viewed as an instability, J. Theor. Biol.26 (1970), 399-415. Zbl1170.92306
  4. [JL] W. Jäger And S. Luckhaus, On explosions of solutions to a system ofpartial differential equations modelling chemotaxis, Trans. Amer. Math. Soc.329 (1992), 819-824. Zbl0746.35002MR1046835
  5. [HV1] M.A. Herrero - J.J.L. Velázquez, Singularity patterns in a chemotaxis model, Math. Ann.306 (1996), 583-623. Zbl0864.35008MR1415081
  6. [HV2] M.A. Herrero - J.J.L. Velázquez, Chemotactic collapse for the Keller-Segel model, J. Math. Biol.35 (1996),177-194. Zbl0866.92009MR1478048
  7. [N] T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci. Appl. (1995), 1-21. Zbl0843.92007MR1361006

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