Exact solutions for a diffusion equation with a nonlinear external force
Abstract
This work is devoted to investigate the solutions of the onedimensional diffusion equation by taking the nonlinear external force F(x,t;ρ)=k(t)x+K/x+κx[ into account. Our investigation is first performed by considering the case α=0 and η=1, which results in a Burgers like equation with a spatial and time dependent external force. After, we consider the case α≠0 and η=α+1 and show that the solution found may be expressed in terms of the qexponential functions present in the Tsallis formalism. In addition, we also discuss the stationary solution for α and η arbitraries.
 Publication:

Physics Letters A
 Pub Date:
 March 2008
 DOI:
 10.1016/j.physleta.2007.12.007
 Bibcode:
 2008PhLA..372.2359Z
 Keywords:

 05.60.k;
 05.40.a;
 66.10.Cb;
 05.10.Gg;
 Transport processes;
 Fluctuation phenomena random processes noise and Brownian motion;
 Diffusion and thermal diffusion;
 Stochastic analysis methods