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Transactions of the American Mathematical Society

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On explosions of solutions to a system of partial differential equations modelling chemotaxis


Authors: W. Jäger and S. Luckhaus
Journal: Trans. Amer. Math. Soc. 329 (1992), 819-824
MSC: Primary 35Q80; Secondary 35B05, 92C45
MathSciNet review: 1046835
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Abstract: A system of partial differential equations modelling chemotactic aggregation is analysed (Keller-Segel model). Conditions on the system of parameters are given implying global existence of smooth solutions. In two space dimensions and radially symmetric situations, explosion of the bacteria concentration in finite time is shown for a class of initial values.


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  • [A1] Wolfgang Alt, Orientation of cells migrating in a chemotactic gradient, Biological growth and spread (Proc. Conf., Heidelberg, 1979) Lecture Notes in Biomath., vol. 38, Springer, Berlin-New York, 1980, pp. 353–366. MR 609371
  • [A2] Wolfgang Alt, Biased random walk models for chemotaxis and related diffusion approximations, J. Math. Biol. 9 (1980), no. 2, 147–177. MR 661424, 10.1007/BF00275919
  • [C] Stephen Childress, Chemotactic collapse in two dimensions, Modelling of patterns in space and time (Heidelberg, 1983) Lecture Notes in Biomath., vol. 55, Springer, Berlin, 1984, pp. 61–66. MR 813704, 10.1007/978-3-642-45589-6_6
  • [G] G. Gerisch et al., Philos. Trans. Roy. Soc. London Ser. B 272 (1975), 181-192.
  • [K-S] E. F. Keller and L. A. Segel, J. Theoret. Biol. 26 (1970),
  • [K] E. F. Keller, Assessing the Keller-Segel model: how has it fared?, Biological growth and spread (Proc. Conf., Heidelberg, 1979) Lecture Notes in Biomath., vol. 38, Springer, Berlin-New York, 1980, pp. 379–387. MR 609374
  • [P-T] M. A. Pozio and A. Tesei, Global existence results for a strongly coupled quasilinear parabolic system, Nonlinear diffusion equations and their equilibrium states, II (Berkeley, CA, 1986) Math. Sci. Res. Inst. Publ., vol. 13, Springer, New York, 1988, pp. 207–216. MR 956088, 10.1007/978-1-4613-9608-6_11
  • [S] Renate Schaaf, Global branches of one-dimensional stationary solutions to chemotaxis systems and stability, Modelling of patterns in space and time (Heidelberg, 1983) Lecture Notes in Biomath., vol. 55, Springer, Berlin, 1984, pp. 341–349. MR 813723, 10.1007/978-3-642-45589-6_27

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1046835-6
Article copyright: © Copyright 1992 American Mathematical Society