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The periodic patch model for population dynamics with fractional diffusion. (English) Zbl 1207.35279
Summary: 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.

MSC:
35R11 Fractional partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)
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