Fractional nonlinear diffusion equation, solutions and anomalous diffusion

A.T. Silva, E.K. Lenzi, L.R. Evangelista, M.K. Lenzi and L.R. da Silva

Physica A: Statistical Mechanics and its Applications, 2007, vol. 375, issue 1, 65-71

Abstract: We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and, in particular, for the last case in the asymptotic limit, we relate these solutions to the Lévy or Tsallis distributions. In addition, from the results presented here a rich class of diffusive processes, including normal and anomalous ones, can be obtained.

Keywords: Fractional diffusion equation; Nonlinear diffusion equation; Anomalous diffusion; Lévy distribution; Tsallis formalism (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:375:y:2007:i:1:p:65-71

DOI: 10.1016/j.physa.2006.09.001

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