Generalized diffusion equation

Jean Pierre Boon and James F. Lutsko

Physica A: Statistical Mechanics and its Applications, 2006, vol. 368, issue 1, 55-62

Abstract: Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker–Planck equation to account for nonclassical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here, we introduce a nonlinear transformation by defining the q-generating function which, when applied to the intermediate scattering function of classical statistical mechanics, yields, in a mathematically systematic derivation, a generalized form of the advection–diffusion equation in Fourier space. Its solutions are discussed and suggest that the q-generating function approach should be a useful method to generalize classical diffusive transport formulations.

Keywords: Diffusion equation; Nonextensive statistics; q-Generating function (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:368:y:2006:i:1:p:55-62

DOI: 10.1016/j.physa.2005.11.054

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