Travelling wave solutions for reaction-diffusion equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 6, 1997, Pages 3417-3426

  Li, Zheng Yuan ^a   Wang, Ming Xin ^b   Wu, Ya Ping ^c   Ye, Qi Xiao ^d  

^a PEKING UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

^c INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS   (China)

^d BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Cross diffusion systems; Explicit solutions; Reaction diffusion systems; Stability of travelling wave solutions; Travelling wave front solutions; Travelling wave solutions

Indexed keywords

EID: 0042546197     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00363-5     Document Type: Article

References (23)

1. MURRAY, J.D., On travelling wave solutions in a model for Belousov-Zhabotinskii reaction, J. Theor. Biol., 56, 329-353 (1976).
2. MURRAY, J.D., Mathematical Biology, Springer-Verlag, 1989.
3. MANORANJAM, V.C. & MITCHELL A., A numerical study of the Belousov-Zhabotinskii reaction using Galerkin finite element methods, J. Math. Biol. 16, 251-260 (1983).
4. YE, QI-XIAO & WANG, MINGXIN, Travelling wave front solutions of Noyes -Field systems for Belousov-Zhabotinskii reaction, Nonlinear Analysis TMA, 1289-1302 (1987).
5. LI, ZHENGYUAN & YE, QI-XIAO, Travelling wave front solutions for reaction-diffusion systems, J. Partial Differential Equations, 4, 1-14 (1991).
6. LI, ZHENGYUAN, The existence of travelling wave front solutions for reaction-diffusion systems, J. Partial Differential Equations, 5, 17-22 (1992).
7. KANEL', YA. I., Existence of travelling wave solutions of a Belousov-Zhabotinskii system, Differentaialnye Uraveniya. 26, 652-660 (1990).
8. KANEL', YA. I., Existence of travelling wave type solutions of the Belousov-Zhabotinskii system of equation II, Sibirskii Matematichskii Zhurnal, 32, 45-79 (1991).
9. LI, ZHENGYUAN & YE, QI-XIAO, Monotonicity of travelling wave solutions for reaction-diffusion systems and its application, Beijing Mathematics, Volume 1, Part 1, 210-223, SCI-TECH Information Services, 1995.
10. WANG, MINGXIN, XIONG, SHULIN & YE, QI-XIAO, Explicit wave front solutions of Noyes-Field systems for the Belousov-Zhabotinskii reaction, J. Math. Anal. Appl., 182, 705-717 (1994).
11. KOZJAKIN, V.S. & KRASNOSEL'SKII, M.A., The method of parameter functionalization in the Hopf bifurcation problem, Nonlinear Analysis TMA, 11, 149-161 (1987).
12. YE, QI-XIAO & WANG, MINGXIN, A note on travelling wave solutions for Belousov -Zhabotinskii chemical reaction, J. Beijing Institute of Technology. 9, No.4, 5-9 (1989).
13. TROY, W.C., The existence of travelling wave front solutions of a model of the Belousov-Zhabotinskii reaction, J. Diff. Eqns, 36, 89-98 (1980).
14. HOSONO, Y. & MIMURA, M., Singular perturbation approach to travelling waves in competing and diffusion species models, J.Math. Kyoto Univ. 22, 435-461 (1982).
15. HOSONO, Y., Travelling waves for some biological systems with density dependent diffusion, Japan J. Appl. Math. 4, 297-359 (1987).
16. IKEDA, H., MIMURA, M., & NISHIURA, Y., Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems, Nonlinear Anal. Theory Methods Appl. 13, 507-526 (1989).
17. NISHIURA, Y., MIMURA, M., IKEDA, H., & FUJII, H., Singular limit analysis of stability of travelling wave solutions in bistable reaction-diffusion systems, SIAM. J.Math Anal., 2 ,85-122 (1990).
18. WU, YAPING, Travelling waves for a class of cross-diffusion systems with small parameters, J.Differential Equations, 123, 1-34 (1995).
19. WU, YAPING, Stability of travelling waves for a class of cross-diffusion systems,preprint.
20. WU, YAPING, Qualitative Studies of Solutions for Some Cross-Diffusion Systems, preprint.
21. KUZNETSOV, Y.A., ANTONOVSKY, M.Ya, BIKTASHEV, V.N. & APONINA, E.A., A cross-diffusion model of forest boundary dynamics, J.Math. Biol. 32, 219-232 (1994).
22. WU, YAPING, The existence of travelling waves for a cross-diffusion model of forest boundary dynamics, Beijing Mathematics, Vol.1, Part 1, 278-287 (1995).
23. WU, YAPING, The stability of travelling waves for a cross-diffusion model of forest boundary dynamics,preprint.