Existence, uniqueness and asymptotic stability of traveling wavefronts in a non-local delayed diffusion equation

Journal of Dynamics and Differential Equations

Volumn 19, Issue 2, 2007, Pages 391-436

  Ma, Shiwang ^a   Wu, Jianhong ^b  

^a NANKAI UNIVERSITY   (China)

^b YORK UNIVERSITY   (Canada)

Author keywords

Asymptotic stability; Comparison principle; Existence; Non local reaction diffusion equation; Traveling wave front; Uniqueness

Indexed keywords

EID: 34249880480     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-006-9065-7     Document Type: Article

References (9)

1. Chen, X. (1997). Existence, uniqueness, and asymptotic stability of traveling waves in non-local evolution equations. Adv. Diff. Eq. 2, 125-160.
2. Faria, T., Huang, W., and Wu, J. (2006). Traveling waves for delayed reactiondiffusion equations with non-local response. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462, 229-261.
3. Gourley, S. A., So, J. W.-H., and Wu, J. H. (2004). Non-locality of reaction-diffusion equations induced by delay: biological modeling and nonlinear dynamics. J. Math. Sci. 124, 5119-5153.
4. Ma, S. W. (2001). Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem. J. Diff. Eq. 171, 294-314.
5. Martin, R. H., and Smith, H. L. (1990) Abstract functional differential equations and reaction-diffusion systems. Trans. Amer. Math. Soc. 321, 1-44.
6. Smith H. L., and Thieme, H. (1991). Strongly order preserving semiflows generated by functional differential equations. J. Diff. Eq. 93, 332-363.
7. Smith, H. L. and Zhao, X. Q. (2000). Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. SIAM J. Math. Anal. 31, 514-534.
8. So, J. W.-H., Wu, J. H., and Zou, X. F. (2001) A reaction-diffusion model for a single species with age structure. I Traveling wavefronts on unbounded domains. Proc. R. Soc. Lond. A, 457, 1841-1853.
9. Wu, J. H. (1996). Theory and Applications of Partial Functional-Differential Equations, Applied Mathematical Science, Vol. 119, Spring-Verlag, New York.