Anisotropic fractional diffusion equation

G.A. Mendes, E.K. Lenzi, R.S. Mendes and L.R. da Silva
Authors registered in the RePEc Author Service: Gilson Mendes, Sr.

Physica A: Statistical Mechanics and its Applications, 2005, vol. 346, issue 3, 271-283

Abstract: We analyze an anisotropic fractional diffusion equation that extends some known diffusion equations by considering a diffusion coefficient with spatial and time dependence, the presence of external forces and time fractional derivatives. We obtain new exact classes of solutions for a linear anisotropic fractional diffusion equation and investigate the time scaling behavior and an asymptotic solution for a nonlinear anisotropic fractional diffusion equation. We connect the asymptotic solution obtained with the distribution that emerges from the nonextensive statistics to the nonlinear case. We also verify different diffusive behavior, for instance, subdiffusion and superdiffusion, in each direction.

Keywords: Anomalous diffusion; Fractional diffusion; Nonlinear diffusion; Diffusion equation (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:346:y:2005:i:3:p:271-283

DOI: 10.1016/j.physa.2004.07.033

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