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International Journal of Differential Equations
Volume 2013 (2013), Article ID 341473, 7 pages
Analysis of a Model Arising from Invasion by Precursor and Differentiated Cells
Department of Mathematics, University of North Carolina Wilmington, Wilmington, NC 28403, USA
Received 9 April 2013; Accepted 7 August 2013
Academic Editor: Zhi-Qiang Wang
Copyright © 2013 Xiaojie Hou. 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.
- A. J. Trewenack and K. A. Landman, “A traveling wave model for invasion by precursor and differentiated cells,” Bulletin of Mathematical Biology, vol. 71, no. 2, pp. 291–317, 2009.
- D. Xu and X.-Q. Zhao, “Bistable waves in an epidemic model,” Journal of Dynamics and Differential Equations, vol. 16, no. 3, pp. 679–707, 2004.
- X.-Q. Zhao and W. Wang, “Fisher waves in an epidemic model,” Discrete and Continuous Dynamical Systems B, vol. 4, no. 4, pp. 1117–1128, 2004.
- P. K. Denman, D. L. S. McElwain, and J. Norbury, “Analysis of travelling waves associated with the modelling of aerosolised skin grafts,” Bulletin of Mathematical Biology, vol. 69, no. 2, pp. 495–523, 2007.
- B. Kaźmierczak and V. Volpert, “Mechano-chemical calcium waves in systems with immobile buffers,” Polish Academy of Sciences, vol. 60, no. 1, pp. 3–22, 2008.
- B. Kazmierczak and V. Volpert, “Travelling calcium waves in systems with non-diffusing buffers,” Mathematical Models & Methods in Applied Sciences, vol. 18, no. 6, pp. 883–912, 2008.
- B. Kaźmierczak and V. Volpert, “Calcium waves in systems with immobile buffers as a limit of waves for systems with nonzero diffusion,” Nonlinearity, vol. 21, no. 1, pp. 71–96, 2008.
- B. Kazmierczak and V. Volpert, “Travelling waves in partially degenerate reaction-diffusion systems,” Mathematical Modelling of Natural Phenomena, vol. 2, no. 2, pp. 106–125, 2007.
- A. Ghazaryan, Y. Latushkin, S. Schecter, and A. J. de Souza, “Stability of gasless combustion fronts in one-dimensional solids,” Archive for Rational Mechanics and Analysis, vol. 198, no. 3, pp. 981–1030, 2010.
- J. Fang and X.-Q. Zhao, “Monotone wavefronts for partially degenerate reaction-diffusion systems,” Journal of Dynamics and Differential Equations, vol. 21, no. 4, pp. 663–680, 2009.
- H. Berestycki and L. Nirenberg, “Travelling fronts in cylinders,” Annales de l'Institut Henri Poincaré, vol. 9, no. 5, pp. 497–572, 1992.
- A. W. Leung, X. Hou, and W. Feng, “Traveling wave solutions for Lotka-Volterra system re-visited,” Discrete and Continuous Dynamical Systems B, vol. 15, no. 1, pp. 171–196, 2011.
- A. I. Volpert, V. A. Volpert, and V. A. Volpert, Traveling Wave Solutions of Parabolic Systems, vol. 140 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1994.
- D. H. Sattinger, “On the stability of waves of nonlinear parabolic systems,” Advances in Mathematics, vol. 22, no. 3, pp. 312–355, 1976.
- W. A. Coppel, Dichotomies in Stability Theory, vol. 629 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1978.