Spreading speeds and traveling waves for nonmonotone integrodifference equations

SIAM Journal on Mathematical Analysis

Volumn 40, Issue 2, 2008, Pages 776-789

  Hsu, Sze Bi ^a   Zhao, Xiao Qiang ^b  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^b MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Integrodifference equations; Linear determinacy; Nonmonotone integral operators; Spreading speeds; Traveling waves

Indexed keywords

INTEGRODIFFERENCE EQUATIONS; LINEAR DETERMINACY; NONMONOTONE INTEGRAL OPERATORS; SPREADING SPEEDS; TRAVELING WAVES;

MATHEMATICAL OPERATORS;

SPEED;

EID: 63849210492     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/070703016     Document Type: Article

References (22)

1. D. G. ARONSON AND H. F. WEINBERGER, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in Partial Differential Equations and Related Topics, J. A. Goldstein, ed., Lecture Notes in Mathematics Ser. 446, Springer-Verlag, Berlin, 1975, pp. 5-49.
2. D. G. ARONSON AND H. F. WEINBERGER, Multidimensional nonlinear diffusion arising in population dynamics, Adv. Math., 30 (1978), pp. 33-76.
3. O. DIEKMANN, Thresholds and traveling waves for the geographical spread of infection, J. Math. Biol., 6 (1978), pp. 109-130.
4. T. FARIA, W. HUANG, AND J. Wu, Traveling waves for delayed reaction-diffusion equations with global response, Proc. Roy. Soc. Lond. Ser. A., 462 (2006), pp. 229-261.
5. J. K. HALE AND H. KOCAK, Dynamics and Bifurcations, Springer-Verlag, New York, 1991.
6. A. HASTINGS, K. CUDDINGTON, K. F. DAVIES, C. J. DUGAW, S. ELMENDORF, A. FREESTONE, S. HARRISON, M. HOLLAND, J. LAMBRINOS, U. MALVADKAR, B. A. MELBOURNE, K. MOORE, C. TAYLOR, AND D. THOMSON, The spatial spread of invasions: New developments in theory and evidence, Ecology Lett., 8 (2005), pp. 91-101.
7. M. KOT, Discrete-time traveling waves: Ecological examples, J. Math. Biol., 30 (1992), pp. 413-436.
8. J. M. LEVINE, E. PACHEPSKY, B. E. KENDALL, S. G. YELENIK, AND J. H. R. LAMBERS, Plant-soil feedbacks and invasive spread, Ecology Lett., 9 (2006), pp. 1005-1014.
9. M. KOT, M. A. LEWIS, AND P. VAN DEN DRIESSCHE, Dispersal data and the spread of invading organisms, Ecology, 77 (1996), pp. 2027-2042.
10. B. LI, H. F. WEINBERGER, AND M. A. LEWIS, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196 (2005), pp. 82-89.
11. X. LIANG AND X.-Q. ZHAO, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math., 60 (2007), pp. 1-40. Erratum: 61 (2008), pp. 137-138.
12. X. LIANG, Y. YI, AND X.-Q. ZHAO, Spreading speeds and traveling waves for periodic evolution systems, J. Differential Equations, 231 (2006), pp. 57-77.
13. R. Lui, Biological growth and spread modeled by systems of recursions, I. Mathematical theory, Math. Biosci., 93 (1989), pp. 269-295.
14. S. MA, Traveling waves for non-local delayed diffusion equations via auxiliary equations, J. Differential Equations, 237 (2007), pp. 259-277.
15. M. NEUBERT AND H. CASWELL, Demography and dispersal: Calculation and sensitivity analysis of invasion speed for structured populations, Ecology, 81 (2000), pp. 1613-1628.
16. C. Ou AND J. Wu, Persistence of wavefronts in delayed nonlocal reaction-diffusion equations, J. Differential Equations, 235 (2007), pp. 219-261.
17. H. R. THIEME, Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread, J. Math. Biol., 8 (1979), pp. 173-187.
18. H. R. THIEME, On a class of Hammerstein integral equations, Manuscripta Math., 29 (1979), pp. 49-84.
19. H. R. THIEME AND X.-Q. ZHAO, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models, J. Differential Equations, 195 (2003), pp. 430-470.
20. H. F. WEINBERGER, Long-time behavior of a class of biological models, SIAM J. Math. Anal., 13 (1982), pp. 353-396.
21. H. F. WEINBERGER, M. A. LEWIS, AND B. LI, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), pp. 183-218.
22. J. Wu AND X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations, 13 (2001), pp. 651-687.