Journal of Applied Mathematics

Global Attractor for a Chemotaxis Model with Reaction Term

Xueyong Chen and Jianwei Shen

Full-text: Open access

Abstract

A chemotaxis model with reproduction term in a bounded domain ΩRn is discussed in this paper, where n=2,3. First, the existence of a global-in-time solution is given, and then a global attractor for this model is obtained.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 536381, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808049

Digital Object Identifier
doi:10.1155/2013/536381

Mathematical Reviews number (MathSciNet)
MR3074332

Zentralblatt MATH identifier
1271.92010

Citation

Chen, Xueyong; Shen, Jianwei. Global Attractor for a Chemotaxis Model with Reaction Term. J. Appl. Math. 2013 (2013), Article ID 536381, 8 pages. doi:10.1155/2013/536381. https://projecteuclid.org/euclid.jam/1394808049


Export citation

References

  • D. Horstmann and M. Winkler, “Boundedness vs. blow-up in a chemotaxis system,” Journal of Differential Equations, vol. 215, no. 1, pp. 52–107, 2005.
  • K. Osaki, T. Tsujikawa, A. Yagi, and M. Mimura, “Exponential attractor for a chemotaxis-growth system of equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 51, no. 1, pp. 119–144, 2002.
  • X. Chen and W. Liu, “Global attractor for a density-dependent sensitivity chemotaxis model,” Acta Mathematica Scientia B, vol. 32, no. 4, pp. 1365–1375, 2012.
  • L. E. Payne and B. Straughan, “Decay for a Keller-Segel chemotaxis model,” Studies in Applied Mathematics, vol. 123, no. 4, pp. 337–360, 2009.
  • R. A. Quinlan and B. Straughan, “Decay bounds in a model for aggregation of microglia: application to Alzheimer's disease senile plaques,” Proceedings of The Royal Society of London A, vol. 461, no. 2061, pp. 2887–2897, 2005.
  • O. Ladyzhenskaya, Attractors for Semigroups and Evolution Equations, Cambridge University Press, Cambridge, UK, 1991.
  • A. Pazy, Semigroups of Linear Operators and Applications to Par-tial Differential Equations, vol. 44 of Applied Mathematical Sci-ences, Springer, New York, NY, USA, 1983.
  • J. K. Hale, Asymptotic Behavior of Dissipative Systems, vol. 25 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1988.
  • A. V. Babin and M. I. Vishik, “Attractors of partial differential evolution equations in an unbounded domain,” Proceedings of the Royal Society of Edinburgh A, vol. 116, no. 3-4, pp. 221–243, 1990.
  • A. Friedman, Partial Differential Equations, Holt Rinehart and Winston, New York, NY, USA, 1969.
  • X. Mora, “Semilinear parabolic problems define semiflows on ${C}^{k}$ spaces,” Transactions of the American Mathematical Society, vol. 278, no. 1, pp. 21–55, 1983.