Fractional diffusion with Neumann boundary conditions: the logistic equation

  title={Fractional diffusion with Neumann boundary conditions: the logistic equation},
  author={Eugenio Montefusco and Benedetta Pellacci and Gianmaria Verzini},
  journal={arXiv: Analysis of PDEs},
Motivated by experimental studies on the anomalous diffusion of biological populations, we introduce a nonlocal differential operator which can be interpreted as the spectral square root of the Laplacian in bounded domains with Neumann homogeneous boundary conditions. Moreover, we study related linear and nonlinear problems exploiting a local realization of such operator as performed in [X. Cabre' and J. Tan. Positive solutions of nonlinear problems involving the square root of the Laplacian… 

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