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Fractional diffusion with Neumann boundary conditions: The logistic equation

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  • Motivated by experimental studies on the anomalous diffusion of biological populations, we study the spectral square root of the Laplacian in bounded domains with Neumann homogeneous boundary conditions. Such operator arises in the continuous limit for long jumps random walks with reflecting barriers. Existence and uniqueness results for positive solutions are proved in the case of indefinite nonlinearities of logistic type by means of bifurcation theory.
    Mathematics Subject Classification: Primary: 35R11; Secondary: 35J65, 92D25, 35B32.

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