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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

The periodic patch model for population dynamics with fractional diffusion

Pages: 1 - 13, Volume 4, Issue 1, February 2011      doi:10.3934/dcdss.2011.4.1

 
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Henri Berestycki - Ecole des Hautes Etudes en Sciences Sociales, CAMS, 54, bd Raspail F-75270 Paris, France (email)
Jean-Michel Roquejoffre - Institut de Mathématiques, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 4, France (email)
Luca Rossi - Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via Trieste, 63 - 35121 Padova, Italy (email)

Abstract: 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, 92D25.

Received: May 2010;      Available Online: October 2010.

 References