EXISTENCE OF TRAVELING WAVE SOLUTIONS IN A HYPERBOLIC-ELLIPTIC SYSTEM OF EQUATIONS

Communications in Mathematical Sciences

Volumn 4, Issue 4, 2006, Pages 731-739

  Mansour, M B A ^a  

^a SOUTH VALLEY UNIVERSITY   (Egypt)

Author keywords

Hyperbolic elliptic system; Singular perturbations; Traveling wave solutions

Indexed keywords

EID: 65249136916     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2006.v4.n4.a3     Document Type: Article

References (16)

1. [1] M. E. Akveld and J. Hulshof, Travelling wave solutions of a fourth-order semilinear diffusion equation, Appl. Math. Letters, 11, 115-120, 1998.
2. [2] W. Alt and M. Dembo, Cytoplasm dynamics and cell motion: two-phase flow models, Math. Biosci., 156, 207-228, 1999.
3. [3] P. Ashwin, M. V. Bbartuccelli, T. J. Bridges and S. A. Gourley, Travelling fronts fot the KPP-Fisher equation with spatio-temporal delay, Z. Angew. Math. Phys., 53, 103-122, 2002.
4. [4] H. M. Byrne, M. A. J. Chaplain, G. J. Pettet and D. L. S. McElwain, A mathematical model of trophoblast invasion, J. Theoret. Med., 1, 275-286, 1999.
5. [5] G. C. Cruywagen and J. D. Murray, On a tissue interaction model for skin pattern formation, J. Nonlin. Sci., 2, 217-240, 1992.
6. [6] N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Diff. Eqn., 31, 53-98, 1979.
7. [7] C. K. R. T. Jones, Geometric Singular Perturbation Theory, Dynamical Systems, eds. R. Johnson, Springer-Verlag, Berlin Heidelberg, 1995.
8. [8] J. A. Landman, G. J. Pettet and D. F. Newgrene, Chemotactic cellular migration: smooth and discontinuous travelling wave solutions, SIAM J. Appl. Math., 63, 1666-1681, 2003.
9. [9] X.-B. Lin, Asymptotic expansion for layer solutions of a singularity perturbed reaction-diffusion system, Trans. Amer. Math. Soc., 348, 713-753, 1996.
10. [10] M. B. A. Mansour, Singularity analysis for travelling wave solutions of degenerate diffusion and transport equations modelling cell motility, PhD Thesis, University of Bonn, 2001.
11. [11] J. D. Murray, Mathematical Biology, 2nd ed., Springer-Verlag, Heidelberg, 1993.
12. [12] M. E. Orme and M. A. J. Chaplain, A mathematical model of vascular tumour growth and invasion, Math. Comput. Modell. 23, 43-60, 1996.
13. [13] G. J. Pettet, H. M. Byrne, D. L. S. McElwain and J. Norbury, A model of wound-healing angiogenesis in soft tissue, Math. Biosci., 136, 35-63, 1996.
14. [14] S. Ruan and D. Xiao, Stability of steady states and existence of travelling waves in a vector-disease model, Proc. R. Soc. Edinb. A 134, 991-1011, 2004.
15. [15] K. Sakamoto, Invariant manifold in singular perturbation problems for ordinary differential equations, Proc. R. Soc. Edinb. A, 116, 45-78, 1990.
16. [16] J. A. Sherratt and J. D. Murray, Mathematical analysis of a basic model for epidermal wound healing, J. Math. Biol., 29, 389-404, 1991.