This work is devoted to investigate the solutions of the one-dimensional 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 q-exponential functions present in the Tsallis formalism. In addition, we also discuss the stationary solution for α and η arbitraries.
Physics Letters A
- Pub Date:
- March 2008
- Transport processes;
- Fluctuation phenomena random processes noise and Brownian motion;
- Diffusion and thermal diffusion;
- Stochastic analysis methods