Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2012, Article ID 956564, 12 pages
http://dx.doi.org/10.1155/2012/956564
Research Article

Blow-Up and Global Existence for a Degenerate Parabolic System with Nonlocal Sources

1Institute of Mathematics and Information Science, Yulin Normal University, Guangxi, Yulin 537000, China
2Institute of Mathematics, Jilin University, Jilin, Changchun 130024, China

Received 25 October 2011; Revised 14 March 2012; Accepted 21 March 2012

Academic Editor: Yuriy Rogovchenko

Copyright © 2012 Ling Zhengqiu and Wang Zejia. 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. M. Escobedo and M. A. Herrero, “Boundedness and blow up for a semilinear reaction-diffusion system,” Journal of Differential Equations, vol. 89, no. 1, pp. 176–202, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuation, Wiley-Interscience, London, UK, 1971.
  3. H. Meinhardt, Models of Biological Pattern Formation, Academic Press, London, UK, 1982.
  4. M. Escobedo and M. A. Herrero, “A semilinear parabolic system in a bounded domain,” Annali di Matematica Pura ed Applicata, vol. 165, pp. 315–336, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. M. Escobedo and H. A. Levine, “Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations,” Archive for Rational Mechanics and Analysis, vol. 129, no. 1, pp. 47–100, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Z. G. Lin and Y. R. Liu, “Uniform blowup profiles for diffusion equations with nonlocal source and nonlocal boundary,” Acta Mathematica Scientia B, vol. 24, no. 3, pp. 443–450, 2004. View at Google Scholar
  7. P. Souplet, “Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source,” Journal of Differential Equations, vol. 153, no. 2, pp. 374–406, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. W. B. Deng, Z. W. Duan, and C. H. Xie, “The blow-up rate for a degenerate parabolic equation with a non-local source,” Journal of Mathematical Analysis and Applications, vol. 264, no. 2, pp. 577–597, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. J. R. Anderson and K. Deng, “Global existence for degenerate parabolic equations with a non-local forcing,” Mathematical Methods in the Applied Sciences, vol. 20, no. 13, pp. 1069–1087, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. X. Wang, “Global existence and finite time blow up for a reaction-diffusion system,” Zeitschrift für Angewandte Mathematik und Physik, vol. 51, no. 1, pp. 160–167, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. H. W. Chen, “Global existence and blow-up for a nonlinear reaction-diffusion system,” Journal of Mathematical Analysis and Applications, vol. 212, no. 2, pp. 481–492, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. V. A. Galaktionov, S. P. Kurdyumov, and A. A. Samarskii, “A parabolic system of quasi-linear equations I,” Differential Equations, vol. 19, pp. 1558–1571, 1983. View at Google Scholar
  13. S. N. Zheng, “Global existence and global non-existence of solutions to a reaction-diffusion system,” Nonlinear Analysis, vol. 39, pp. 327–340, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. F. C. Li, S. X. Huang, and C. H. Xie, “Global existence and blow-up of solutions to a nonlocal reaction-diffusion system,” Discrete and Continuous Dynamical Systems A, vol. 9, no. 6, pp. 1519–1532, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. W. B. Deng, Y. X. Li, and C. H. Xie, “Blow-up and global existence for a nonlocal degenerate parabolic system,” Journal of Mathematical Analysis and Applications, vol. 277, no. 1, pp. 199–217, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. Z. Yang, “Nonexistence of positive solutions to a quasi-linear elliptic equation and blow-up estimates for a nonlinear heat equation,” The Rocky Mountain Journal of Mathematics, vol. 36, no. 4, pp. 1399–1414, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. P. Souplet, “Blow-up in nonlocal reaction-diffusion equations,” Society for Industrial and Applied Mathematics Journal on Mathematical Analysis, vol. 29, no. 6, pp. 1301–1334, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH