Articles

REMARK ON CRITICAL SPEED OF TRAVELING WAVEFRONTS FOR NICHOLSON'S BLOWFLIES EQUATION WITH DIFFUSION

  • WEI De ,
  • WU Jiao-Yu ,
  • MEI Ming
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  • Department of Information and Computation, Nanchang Hangkong University, Nanchang 330068, China|School of Computer Engineering and Technology, Guangdong Institute of Science and Technology, Guangzhou 510640, China|Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec, J4P 3P2, Canada  Department of Mathematics and Statistics, McGill University, Montreal |H3G 1M8, Canada

Received date: 2008-06-06

  Online published: 2010-09-20

Supported by

The work was supported  by Natural Sciences and Engineering Research Council of Canada under the  NSERC grant RGPIN 354724-08.

Abstract

This note is devoted to the study on the traveling wavefronts to the Nicholson's blowflies equation with diffusion, a time-delayed reaction-diffusion equation. For the critical speed of traveling waves, we give a detailed analysis on its location and asymptotic behavior with respect to the mature age.

Cite this article

WEI De , WU Jiao-Yu , MEI Ming . REMARK ON CRITICAL SPEED OF TRAVELING WAVEFRONTS FOR NICHOLSON'S BLOWFLIES EQUATION WITH DIFFUSION[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1561 -1566 . DOI: 10.1016/S0252-9602(10)60149-X

References


[1]  Gurney W S C, Blythe S P, Nisbet R M. Nicholson's blowflies revisited. Nature, 1980, 287:  17--21


[2] Liang D, Wu J.  Traveling waves and numerical approximations in a reaction-diffusion equation with nonlocal delayed effect. J Nonlinear Sci, 2003, 13: 289--310


[3] Lin C K, Mei M. On  traveling wavefronts of Nicholson's blowflies equation with diffusion. Proc Royal Soc Edinburgh, 2010, 140A: 135--152


[4] Mei M, So J W-H, Li M Y,  Shen S S P. Asymptotic stability of traveling waves for the Nicholson's blowflies equation with diffusion. Proc Royal Soc Edinbourgh, 2004, 134A: 579--594


[5] Mei M, So J W-H. Stability of strong traveling waves for a nonlocal time-delayed reaction-diffusion equation. Proc Royal Soc Edinburgh, 2008, 138A: 551--568


[6] Nicholson A J.  Competition for foodamongst Lucilia Cuprina larvae//Proceeding of the VIII International Congress of Entomology. Stockholm, 1948: 277--281


[7] Nicholson A J.  An outline of the dynamics of animal populations. Aust J Zool, 1954,  2: 9--65


[8] Ou C, Wu J.  Persistence of wavefronts in delayed non-local reaction-diffusion equations. J Differ Equ, 2007, 235: 219--261


[9] So J W-H, Wu J, Yang Y. Numerical Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation. Appl Math Comp, 2000, 111: 53--69


[10] So J W-H, Yang Y. Direchlet problem for the diffusive Nicholson's blowflies equation. J Differ Equ, 1998, 150: 317--348


[11] So J W-H, Zou X.  Traveling waves for the diffusive Nicholson's blowflies equation. Appl Math Comp, 2001, 122: 385--392


[12]  Thieme H R.  Mathematics in Population Biology. Princeton: Princeton University Press, 2003


[13]  Thieme H, Zhao X Q. Asymptotic speeds of spread and traveling waves for integral equation and delayed reaction-diffusion models. J Differ Equ, 2003, 195: 430--370


[14]  Wu J -H. Theory and Applications of Partial Functional-Differential Equations. Appl Math Sci, Vol  119. New York: Springer-Verlag, 1996


[15]  Wu J Y, Wei D, Mei M. Analysis on critical speed of traveling waves. Appl Math Letters, 2007, 20: 712--718


[16]  Zhao X Q. Dynamical Systems in Population Biology. New York: Springer-Verlag, 2003


[17]  Mo J, Zhang W, He M. Asymptotic method of traveling wave solutions for a class of nonlinear reaction-diffuison equations. Acta Math Sci, 2007, 27B(4): 777--780


[18]  Liu H, Pan T. Pointwise convergence rate of vanishing viscosity approximation for scalar conservation laws with boundary. Acta Math Sci, 2009, 29B(1): 111--128

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