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The generalized Cattaneo equation for the description of anomalous transport processes. (English) Zbl 0941.82046
Summary: 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, nonlocal 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, the authors recover the mean-square displacement which is characteristic for these anomalous processes. As expected the short-time behaviour is modified in comparison to generalized diffusion equations.

##### MSC:
 82C70 Transport processes (time-dependent statistical mechanics) 35K99 Parabolic equations and systems