Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 186125, 7 pages
http://dx.doi.org/10.1155/2014/186125
Research Article

The Global Existence of Solutions in Time for a Chemotaxis Model with Two Chemicals

1Department of Basic Courses, Beijing Union University, Beijing 100101, China
2School of Sciences, Zhejiang A&F University, Hangzhou, Zhejiang 311300, China

Received 6 April 2014; Revised 21 May 2014; Accepted 27 May 2014; Published 16 June 2014

Academic Editor: Zhidong Teng

Copyright © 2014 Qian Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Keller and L. Segel, “Initiation of slime mold aggregation viewed as an instability,” Journal of Theoretical Biology, vol. 26, pp. 399–415, 1970. View at Publisher · View at Google Scholar
  2. K. Osaki and A. Yagi, “Finite dimensional attractor for one-dimensional Keller-Segel equations,” Funkcialaj Ekvacioj, vol. 44, no. 3, pp. 441–469, 2001. View at Google Scholar · View at MathSciNet
  3. D. Horstmann, “From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. I,” Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 105, pp. 103–165, 2003. View at Google Scholar
  4. D. Horstmann, “From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II,” Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 106, no. 2, pp. 51–69, 2004. View at Google Scholar · View at MathSciNet
  5. T. Hillen and K. J. Painter, “A user's guide to PDE models for chemotaxis,” Journal of Mathematical Biology, vol. 58, no. 1-2, pp. 183–217, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  6. K. J. Painter, P. K. Maini, and H. G. Othmer, “Development and applications of a model for cellular response to multiple chemotactic cues,” Journal of Mathematical Biology, vol. 41, no. 4, pp. 285–314, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  7. A. M. Turing, “The chemical basis for morphogenesis,” Philosophical Transactions of the Royal Society of London B, vol. 237, pp. 37–72, 1952. View at Google Scholar
  8. R. Dillon, P. K. Maini, and H. G. Othmer, “Pattern formation in generalized Turing systems. I. Steady-state patterns in systems with mixed boundary conditions,” Journal of Mathematical Biology, vol. 32, no. 4, pp. 345–393, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  9. H. G. Othmer and J. A. Aldridge, “The effects of cell density and metabolite flux on cellular dynamics,” Journal of Mathematical Biology, vol. 5, no. 2, pp. 169–200, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  10. H. Amann, “Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems,” Differential and Integral Equations, vol. 3, no. 1, pp. 13–75, 1990. View at Google Scholar · View at MathSciNet
  11. H. Amann, “Dynamic theory of quasilinear parabolic systems. III. Global existence,” Mathematische Zeitschrift, vol. 202, no. 2, pp. 219–250, 1989. View at Publisher · View at Google Scholar · View at MathSciNet