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Singularity patterns in a chemotaxis model

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References

  • [A1] W. Alt: Orientation of cells migrating in a chemotatic gradient. Lectures Notes in Biomath. vol.38, Springer-Verlag (1980), 353–366.

    Google Scholar 

  • [A2] W. Alt: Biased random walk models for chemotaxis and related diffusion approximations. J. Math. Biol.9 (1980), 147–177.

    Google Scholar 

  • [AV] SB. Angenent, JJ.L. Velázquez: Degenerate neckpinches in mean curvature flow. To appear.

  • [BGG] E. Bombieri, E. De Giorgi, E. Giusti: Minimal cones and the Bernstein problem. Inventiones Math.7 (1969), 243–268.

    Google Scholar 

  • [C] S. Childress: Chemotactic collapse in two dimensions. Lectures Notes in Biomath. vol.55, Springer-Verlag (1984), 61–66.

    Google Scholar 

  • [CP] S. Childress, JK. Percus: Nonlinear aspects of chemotaxis. Math. Biosci.56 (1981), 217–237.

    Google Scholar 

  • [DN] J.I. Diaz, T. Nagai: Symmetrization in a parabolic-elliptic system related to chemotaxis. Adv. Math. Sci. Appl., to appear.

  • [GK] Y. Giga, RV. Kohn: Asymptotically self-similar blow-up of semilinear heat equations. Comm. Pure. Appl. Math.38 (1985), 297–319.

    Google Scholar 

  • [HV1] MA. Herrero, JJL. Velazquez: Explosion des solutions d'équations paraboliques semilinéaires supercritiques. C.R. Acad. Sci. Paris t.319, I (1994), 141–145.

    Google Scholar 

  • [HV2] MA. Herrero, J JL. Velazquez: On the melting of ice balls. SIAM J. Math. Anal, to appear.

  • [JL] W. Jäger, S. Luckhaus: On explosions of solutions to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc., vol.329, n. 2 (1992), 819–824.

    Google Scholar 

  • [KS] EF. Keller, LA. Segel: Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol.26 (1970), 399–415.

    PubMed  Google Scholar 

  • [N] T. Nagai: Blow-up of radially symmetric solutions to a chemotaxis system. To appear in Adv. Math. Sci. Appl.

  • [Na] V. Nanjundiah: Chemotaxis, signal relaying and aggregation morphology. J. Theor. Biol.42 (1973), 63–105.

    Google Scholar 

  • [V] JJL. Velazquez: Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow. Annali Scuola Normale Superiore di Pisa, Serie IV, vol.XXI, Fasc. 4 (1994), 595–628.

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, E-28040, Madrid, Spain

    Miguel A. Herrero & Juan J. L. Velázquez

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  1. Miguel A. Herrero
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  2. Juan J. L. Velázquez
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Partially supported by DGICYT Grant PB93-0438

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Herrero, M.A., Velázquez, J.J.L. Singularity patterns in a chemotaxis model. Math. Ann. 306, 583–623 (1996). https://doi.org/10.1007/BF01445268

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