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Zbl 0941.82046
Compte, Albert; Metzler, Ralf
The generalized Cattaneo equation for the description of anomalous transport processes. (English)
[J] J. Phys. A, Math. Gen. 30, No.21, 7277-7289 (1997). ISSN 0305-4470

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 2000:: *82C70 Transport processes
35K99 Parabolic equations and systems

Keywords: Cattaneo equation; anomalous transport; continuous time random walks; nonlocal transport theory; delayed flux-force relation; long-time limit; short-time behaviour; generalized diffusion equations

Cited in: Zbl 1173.76339

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