Travelling wave solutions in delayed reaction diffusion systems with partial monotonicity

Acta Mathematicae Applicatae Sinica

Volumn 22, Issue 2, 2006, Pages 243-256

  Huang, Jian Hua ^a   Zou, Xing Fu ^b  

^a NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

^b MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Partial monotonicity; Schauder's fixed point theorem; Travelling wave fronts; Upper lower solution

Indexed keywords

EID: 33645660285     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/s10255-006-0300-0     Document Type: Article

References (21)

1. Britton, N.F. Reaction diffusion equations and their application to biology. Academic Press, New York, 1986
2. Fife, P.C. Mathematical aspects of reaction and diffusion systems. Lecture Notes in Biomathematics, Vol. 28, Springer-Verlag, Berlin, New York, 1979
3. Gardner, R. Review on travelling wave solutions of Parabolic Systems by A. I. Volpert, V. A. Volpert and V. A. Volpert. Bull. Amer. Math. Soc., 32: 446-452 (1995)
4. Gourley, S.A. Wave front solutions of a diffusive delay model for population of Daphnia magna. Comp. Math. Appl., 42: 1421-1430 (2001)
5. Huang, J., Zou, X. Travelling wavefronts in diffusive and cooperative lotka-volterra system with delays. J. Math. Anal. Appl., 271: 455-466 (2002)
6. Huang, J., Zou, X. Existence of travelling wavefronts of delayed reaction diffusion systems without monotonicity. Disc. Conti. Dynam. Syst. (series A), 9: 925-936 (2003)
7. Huang, W. Monotonicity of heteroclinic orbits and spectral properties of variational equations for delay differential equations. J. Differential Equations, 162: 91-139 (2000)
8. Ma, S. Travelling wavefronts for delayed reaction-diffusion systems via a fixed point theorem. J. Differential Equations, 171: 294-314 (2001)
9. Murray J. D. Murray. Mathematical Biology, Springer-Verlag, New York, 1989
10. Pao, C.V. Nonlinear parabolic and elliptic equations. New York, Plenum Press, 1992
11. Schaaf, K. Asymptotic behavior and travelling wave solutions for parabolic functional differential equations. Trans. Amer. Math. Soc., 302: 587-615 (1987)
12. Smith, H.L., Thieme, H.R. Monotone semiflows in scalar non-quasimonotone functional differential equations. J. Math. Anal. Appl., 150: 289-306 (1990)
13. Smith, H.L., Thieme, H.R. Strongly order preserving semiflows generated by functional differential equations. J. Differential Equations, 93: 322-363 (1991)
14. Smith, H.L., Zhao, X.Q. Global asymptotic stability of travelling waves in delayed reaction-diffusion equations. SIAM J. Math. Anal., 31: 514-534 (2000)
15. So, J. W.H., Wu, J., Zou, X. A reaction diffusion model for a single species with age structure -I. Travelling wave fronts on unbounded domains. Proc. Royal Soc. London, Ser. A, 457: 1841-1854, 2001
16. So, J. W.-H., Zou, X. Travelling waves for the diffusive Nicholson's blowflies equation. Appl. Math. Compt., 122: 385-392 (2001)
17. Volpert, A.I., Volpert, V.A., Volpert, V.A. Travelling wave solutions of parabolic Systems. Translations of mathematical monographs Vol. 140, Amer. math. Soc., Providence, 1994
18. Ye, Q., Li, Y. Introduction of reaction diffusion equations. Academy Press, BeiJing, 1985
19. Wu, J., Zou, X. Travelling wave fronts of reaction diffusion systems with delay. J Dynam. Diff. Eqns., 13(3): 651-687 (2001)
20. Zeidler, E. Nonlinear functional analysis and its applications, I, Fixed-point Theorems. Springer-Verlag, New York, New York, 1986
21. Zou, X., Wu, J. Existence of travelling wavefronts in delayed reaction-diffusion system via monotone iteration method. Proc. Amer. Math. Soc., 125: 2589-2598 (1997)