Nonlinear diffusion under a time dependent external force: q-maximum entropy solutions |
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Authors: | C Giordano AR Plastino M Casas A Plastino |
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Institution: | (1) Faculty of Astronomy and Geophysics, National University La Plata, CC 727, 1900 La Plata, Argentina, AR;(2) Argentine National Research Council (CONICET), CC 727, 1900 La Plata, Argentina, AR;(3) Departament de Fısica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain, ES;(4) Department of Physics, National University La Plata, CC 727, 1900 La Plata, Argentina, AR |
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Abstract: | Nonlinear diffusion equations provide useful models for a number of interesting phenomena, such as diffusion processes in
porous media. We study here a family of nonlinear Fokker-Planck equations endowed both with a power-law nonlinear diffusion
term and a drift term with a time dependent force linear in the spatial variable. We show that these partial differential
equations exhibit exact time dependent particular solutions of the Tsallis maximum entropy (q-MaxEnt) form. These results constitute generalizations of previous ones recently discussed in the literature C. Tsallis,
D.J. Bukman, Phys. Rev. E 54, R2197 (1996)], concerning q-MaxEnt solutions to nonlinear Fokker-Planck equations with linear, time independent drift forces. We also show that the present
formalism can be used to generate approximate q-MaxEnt solutions for nonlinear Fokker-Planck equations with time independent drift forces characterized by a general spatial
dependence.
Received 25 April 2001 and Received in final form 6 June 2001 |
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Keywords: | PACS 66 10 Cb Diffusion and thermal diffusion – 05 20 -y Classical statistical mechanics – 05 60 -k Transport processes – 05 40 -a Fluctuation phenomena random processes noise and Brownian motion |
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