Existence and nonexistence of monotone traveling waves for the delayed Fisher equation

Journal of Differential Equations

Volumn 249, Issue 3, 2010, Pages 728-745

  Kwong, Man Kam ^a   Ou, Chunhua ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Delay; Fisher equation; Traveling wavefronts

Indexed keywords

EID: 77952955069     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2010.04.017     Document Type: Article

References (16)

1. Bocharov G., Hadeler K.P. Structured population models, conservation laws, and delay equations. J. Differential Equations 2000, 168(1):212-237.
2. Faria T., Huang W., Wu J. Travelling waves for delayed reaction-diffusion equations with global response. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2006, 462(2065):229-261.
3. Fisher R.A. The wave of advance of advantageous genes. Ann. of Eugenics 1937, 7:335-369.
4. Gurney W.S.C., Blythe S.P., Nisbet R.M. Nicholson's blowflies revisited. Nature 1980, 287:17-21.
5. Gourley S.A. Travelling front solutions of a nonlocal Fisher equation. J. Math. Biol. 2000, 41(3):272-284.
6. Hadeler K.P. Neutral delay equations from and for population dynamics. Proc. Colloq. Qual. Theory Differ. Equ. 2008, vol. 8. Electron. J. Qual. Theory. Differ. Equ., Szeged, 18 pp.
7. Hadeler K.P., Bocharov G. Where to put delays in population models, in particular in the neutral case. Can. Appl. Math. Q. 2003, 11(2):159-173.
8. Hutchinson G.E. Circular causal systems in ecology. Ann. New York Acad. Sci. 1948, 50:221-246.
9. Kolmogoroff A., Petrovsky I., Piscounoff N. Etude de l'equation de la diffusion avec croissance de la quantitite de matiere et son application a un probleme biologique. Bull. Univ. Moscou Ser. Internationale Sec. A 1937, 1:1-25.
10. Liang X., Zhao X. Asymptotic speeds of spread and traveling waves for monotone semiflows with applications. Comm. Pure Appl. Math. 2007, 60(1):1-40.
11. Ou C., Wu J. Persistence of wavefronts in delayed nonlocal reaction-diffusion equations. J. Differential Equations 2007, 235(1):219-261.
12. Ou C., Wu J. Traveling wavefronts in a delayed food-limited population model. SIAM J. Math. Anal. 2007, 39(1):103-125.
13. Schaaf K.W. Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations. Trans. Amer. Math. Soc. 1987, 302(2):587-615.
14. So J.W.-H., Wu J., Zou X. A reaction-diffusion model for a single species with age structure: (I) Traveling wavefronts on unbounded domains. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2001, 457:1841-1853.
15. Wang Z., Li W., Ruan S. Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays. J. Differential Equations 2006, 222(1):185-232.
16. Wu J., Zou X. Traveling wave fronts of reaction-diffusion systems with delay. J. Dynam. Differential Equations 2001, 13(3):651-687.