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Abstract and Applied Analysis
Volume 2008, Article ID 239870, 19 pages
http://dx.doi.org/10.1155/2008/239870
Research Article

An Existence Result to a Strongly Coupled Degenerated System Arising in Tumor Modeling

1Faculté des Sciences, Université de Blida, BP 270, Blida 09000, Algeria
2Ecole Polytechnique, CMAP, CNRS, 91128 Palaiseau Cedex, France
3Faculté de Mathématiques, Université des Sciences et de la Technologie Houari Boumediene, BP 32 El Alia, Alger 16111, Algeria

Received 21 March 2008; Revised 25 August 2008; Accepted 30 October 2008

Academic Editor: Nobuyuki Kenmochi

Copyright © 2008 L. Hadjadj 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. C. J. W. Breward, H. M. Byrne, and C. E. Lewis, “The role of cell-cell interactions in a two-phase model for avascular tumour growth,” Journal of Mathematical Biology, vol. 45, no. 2, pp. 125–152, 2002. View at Publisher · View at Google Scholar · View at PubMed · View at Zentralblatt MATH · View at MathSciNet
  2. C. J. W. Breward, H. M. Byrne, and C. E. Lewis, “A multiphase model describing vascular tumour growth,” Bulletin of Mathematical Biology, vol. 65, no. 4, pp. 609–640, 2003. View at Publisher · View at Google Scholar · View at PubMed
  3. H. M. Byrne, J. R. King, D. L. S. McElwain, and L. Preziosi, “A two-phase model of solid tumour growth,” Applied Mathematics Letters, vol. 16, no. 4, pp. 567–573, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. M. Byrne and L. Preziosi, “Modelling solid tumour growth using the theory of mixtures,” Mathematical Medicine and Biology, vol. 20, no. 4, pp. 341–366, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. T. L. Jackson and H. M. Byrne, “A mechanical model of tumor encapsulation and transcapsular spread,” Mathematical Biosciences, vol. 180, no. 1, pp. 307–328, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. Preziosi, Cancer Modelling and Simulation, Mathematical Biology and Medicine Series, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2003. View at Zentralblatt MATH · View at MathSciNet
  7. D. Le, “Cross diffusion systems on n spatial dimensional domains,” in Proceedings of the 5th Mississippi State Conference on Differential Equations and Computational Simulations (Mississippi State, MS, 2001), vol. 10 of Electronic Journal of Differential Equations, pp. 193–210, Southwest Texas State University, San Marcos, Tex, USA, 2003. View at Zentralblatt MATH · View at MathSciNet
  8. P. Laurençot and D. Wrzosek, “A chemotaxis model with threshold density and degenerate diffusion,” in Nonlinear Elliptic and Parabolic Problems, vol. 64 of Progress in Nonlinear Differential Equations and Their Applications, pp. 273–290, Birkhäuser, Basel, Switzerland, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. L. Chen and A. Jüngel, “Analysis of a parabolic cross-diffusion population model without self-diffusion,” Journal of Differential Equations, vol. 224, no. 1, pp. 39–59, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. Galiano, A. Jüngel, and J. Velasco, “A parabolic cross-diffusion system for granular materials,” SIAM Journal on Mathematical Analysis, vol. 35, no. 3, pp. 561–578, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet