On explosions of solutions to a system of partial differential equations modelling chemotaxis
HTML articles powered by AMS MathViewer
- by W. Jäger and S. Luckhaus PDF
- Trans. Amer. Math. Soc. 329 (1992), 819-824 Request permission
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.References
- 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
- Wolfgang Alt, Biased random walk models for chemotaxis and related diffusion approximations, J. Math. Biol. 9 (1980), no. 2, 147–177. MR 661424, DOI 10.1007/BF00275919
- 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, DOI 10.1007/978-3-642-45589-6_{6} G. Gerisch et al., Philos. Trans. Roy. Soc. London Ser. B 272 (1975), 181-192. E. F. Keller and L. A. Segel, J. Theoret. Biol. 26 (1970),
- 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
- 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, DOI 10.1007/978-1-4613-9608-6_{1}1
- 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, DOI 10.1007/978-3-642-45589-6_{2}7
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 819-824
- MSC: Primary 35Q80; Secondary 35B05, 92C45
- DOI: https://doi.org/10.1090/S0002-9947-1992-1046835-6
- MathSciNet review: 1046835