The nonlinear diffusion equation ∂t∂ρ=DΔ~ρν is analyzed here, where Δ~≡rd−11∂r∂rd−1−θ∂r∂, and d, θ and ν are real parameters.
This equation unifies the anomalous diffusion equation on fractals (ν=1)
and the spherical anomalous diffusion for porous media (θ=0). Exact
point-source solution is obtained, enabling us to describe a large class of
subdiffusion (θ>(1−ν)d), normal diffusion (θ=(1−ν)d) and
superdiffusion (θ<(1−ν)d). Furthermore, a thermostatistical basis
for this solution is given from the maximum entropic principle applied to the
Tsallis entropy.Comment: 3 pages, 2 eps figure