\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

The periodic patch model for population dynamics with fractional diffusion

Abstract Related Papers Cited by
  • Fractional diffusions arise in the study of models from population dynamics. In this paper, we derive a class of integro-differential reaction-diffusion equations from simple principles. We then prove an approximation result for the first eigenvalue of linear integro-differential operators of the fractional diffusion type, and we study from that the dynamics of a population in a fragmented environment with fractional diffusion.
    Mathematics Subject Classification: Primary: 35R11; Secondary: 35B40, 35K57, 92D25.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    H. Berestycki, Le nombre de solutions de certains problèmes semi-linéaires elliptiques, J. Funct. Anal, 40 (1981), 1-29.doi: doi:10.1016/0022-1236(81)90069-0.

    [2]

    H. Berestycki, F. Hamel and N. Nadirashvili, Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys., 253 (2005), 451-480.doi: doi:10.1007/s00220-004-1201-9.

    [3]

    H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence, J. Math. Biol, 51 (2005), 75-113.doi: doi:10.1007/s00285-004-0313-3.

    [4]

    H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating travelling fronts, J. Math. Pures Appl, 84 (2005), 1101-1146.doi: doi:10.1016/j.matpur.2004.10.006.

    [5]

    J.-M. Bony, P. Courrège and P. Priouret, Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum, Ann. Inst. Fourier, 18 (1968), 369-521.

    [6]

    X. Cabré and J.-M. Roquejoffre, Propagation de fronts dans les équations de Fisher-KPP avec diffusion fractionnaire, C. R. Math. Acad. Sci. Paris, 347 (2009), 1361-1366.

    [7]

    Y. Capdeboscq, Homogenization of a neutronic critical diffusion problem with drift, Proc. Royal Soc. Edinburgh, 132 (2002), 567-594.doi: doi:10.1017/S0308210500001785.

    [8]

    P. Constantin, A. Kiselev, L. Ryzhik and A. Zlatos, Diffusion and mixing in fluid flow, Annals of Math., 168 (2008), 643-674.doi: doi:10.4007/annals.2008.168.643.

    [9]

    J. Coville, PhD thesis, 2003.

    [10]

    P. C. Fife, "Mathematical Aspects of Reacting and Diffusing Systems," Springer-Verlag, 1979.

    [11]

    A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, Etude de l'équation de diffusion avec accroissement de la quantité de matière, et son application à un problème biologique, Bjul. Moskowskogo Gos. Univ., 17 (1937), 1-26.

    [12]

    J. D. Murray, "Mathematical Biology," 2nd edition, Biomathematics, 19, Springer-Verlag, Berlin, 1993.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(166) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return