6 research outputs found
Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions
We consider the nonlinear Fokker-Planck-like equation with fractional
derivatives . Exact
time-dependent solutions are found for
(). By considering the long-distance {\it asymptotic}
behavior of these solutions, a connection is established, namely
(), with the solutions optimizing
the nonextensive entropy characterized by index . Interestingly enough,
this relation coincides with the one already known for L\'evy-like
superdiffusion (i.e., and ). Finally, for
we obtain which differs from the value
corresponding to the solutions available in the literature (
porous medium equation), thus exhibiting nonuniform convergence.Comment: 3 figure
Anomalous diffusion with absorption: Exact time-dependent solutions
Recently, analytical solutions of a nonlinear Fokker-Planck equation
describing anomalous diffusion with an external linear force were found using a
non extensive thermostatistical Ansatz. We have extended these solutions to the
case when an homogeneous absorption process is also present. Some peculiar
aspects of the interrelation between the deterministic force, the nonlinear
diffusion and the absorption process are discussed.Comment: RevTex, 16 pgs, 4 figures. Accepted in Physical Review