Eur. Phys. J. B 22, 361-368 (2001)
https://doi.org/10.1007/s100510170114

Nonlinear diffusion under a time dependent external force: q-maximum entropy solutions

¹ Faculty of Astronomy and Geophysics, National University La Plata, CC 727, 1900 La Plata, Argentina
² Argentine National Research Council (CONICET), CC 727, 1900 La Plata, Argentina
³ Departament de Física, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain
⁴ Department of Physics, National University La Plata, CC 727, 1900 La Plata, Argentina

Corresponding author: ^a plastino@venus.fisica.unlp.edu.ar

Received: 25 April 2001
Revised: 6 June 2001
Published online: 15 August 2001

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.