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February  2011, 4(1): 1-13. doi: 10.3934/dcdss.2011.4.1

The periodic patch model for population dynamics with fractional diffusion

Henri Berestycki 1, , Jean-Michel Roquejoffre 2, and  Luca Rossi 3,

1. 

Ecole des Hautes Etudes en Sciences Sociales, CAMS, 54, bd Raspail F-75270 Paris, France
2. 

Institut de Mathématiques, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 4, France
3. 

Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via Trieste, 63 - 35121 Padova, Italy

Received  May 2010 Published  October 2010

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.
Keywords: Fractional diffusion, reaction-diffusion equation, KPP nonlinearity, persistence..
Mathematics Subject Classification: Primary: 35R11; Secondary: 35B40, 35K57, 92D2.
Citation: Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi. The periodic patch model for population dynamics with fractional diffusion. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 1-13. doi: 10.3934/dcdss.2011.4.1
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show all references

References:
[1]

J. Funct. Anal, 40 (1981), 1-29. doi: doi:10.1016/0022-1236(81)90069-0.  Google Scholar

[2]

Comm. Math. Phys., 253 (2005), 451-480. doi: doi:10.1007/s00220-004-1201-9.  Google Scholar

[3]

J. Math. Biol, 51 (2005), 75-113. doi: doi:10.1007/s00285-004-0313-3.  Google Scholar

[4]

J. Math. Pures Appl, 84 (2005), 1101-1146. doi: doi:10.1016/j.matpur.2004.10.006.  Google Scholar

[5]

Ann. Inst. Fourier, 18 (1968), 369-521.  Google Scholar

[6]

C. R. Math. Acad. Sci. Paris, 347 (2009), 1361-1366.  Google Scholar

[7]

Proc. Royal Soc. Edinburgh, 132 (2002), 567-594. doi: doi:10.1017/S0308210500001785.  Google Scholar

[8]

Annals of Math., 168 (2008), 643-674. doi: doi:10.4007/annals.2008.168.643.  Google Scholar

[9]

2003. Google Scholar

[10]

Springer-Verlag, 1979.  Google Scholar

[11]

Bjul. Moskowskogo Gos. Univ., 17 (1937), 1-26. Google Scholar

[12]

Biomathematics, 19, Springer-Verlag, Berlin, 1993.  Google Scholar

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