The generalized Cattaneo equation for the description of anomalous transport processes

@article{Compte1997TheGC,
  title={The generalized Cattaneo equation for the description of anomalous transport processes},
  author={Albert Compte and Ralf Metzler},
  journal={Journal of Physics A},
  year={1997},
  volume={30},
  pages={7277-7289}
}
The Cattaneo equation, which describes a diffusion process with a finite velocity of propagation, is generalized to describe anomalous transport. Three possible generalizations are proposed, each one supported by a different scheme: continuous time random walks, non-local transport theory, and delayed flux-force relation. The properties of these generalizations are studied in both the long-time and the short-time regimes. In the long-time limit, we recover the mean-square displacement which is… 
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