The periodic patch model for population dynamics with fractional diffusion

Henri Berestycki; Jean-Michel Roquejoffre; Luca Rossi

doi:10.3934/dcdss.2011.4.1

Article Contents

2011, Volume 4, Issue 1: 1-13. Doi: 10.3934/dcdss.2011.4.1

This issue Previous Article Preface Next Article Large-time asymptotics of the generalized Benjamin-Ono-Burgers equation

The periodic patch model for population dynamics with fractional diffusion

1.
Ecole des Hautes Etudes en Sciences Sociales, CAMS, 54, bd Raspail F-75270 Paris
2.
Institut de Mathématiques, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 4
3.
Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via Trieste, 63 - 35121 Padova

Received: May 2010

Published: February 2011

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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.

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Mathematics Subject Classification: Primary: 35R11; Secondary: 35B40, 35K57, 92D25.

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