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Fractional diffusion limits of non-classical transport equations

  • * Corresponding author: Martin Frank

    * Corresponding author: Martin Frank 
The first author is supported by the German research foundation DFG under grant FR2841/6-1.
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  • We establish asymptotic diffusion limits of the non-classical transport equation derived in [12]. By introducing appropriate scaling parameters, the limits will be either regular or fractional diffusion equations depending on the tail behaviour of the path-length distribution. Our analysis is based on a combination of the Fourier transform and a moment method. We put special focus on dealing with anisotropic scattering, which compared to the isotropic case makes the analysis significantly more involved.

    Mathematics Subject Classification: Primary: 82B40, 80M35; Secondary: 35R11.


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