Fractional and nonlinear diffusion equation: additional results

L.R. da Silva, L.S. Lucena, E.K. Lenzi, R.S. Mendes and Kwok Sau Fa

Physica A: Statistical Mechanics and its Applications, 2004, vol. 344, issue 3, 671-676

Abstract: We investigate the solutions of a generalized diffusion equation which extends some known equations such as the fractional diffusion equation and the porous medium equation. We start our study by considering the linear case and the nonlinear case afterward. The linear case is analyzed taking fractional time and spatial derivatives into account. In this context, we also discuss the modifications that emerge by considering a diffusion coefficient given by D(x)∝|x|−θ. For the nonlinear case accomplishing the fractional time derivative, we discuss scaling behavior of the time and the asymptotic for the solution of the nonlinear fractional diffusion equation. In this case, the connection between the asymptotic solution found here and the nonextensive Tsallis statistics is performed.

Keywords: Anomalous diffusion; Nonlinear diffusion equation (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437104008155
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:344:y:2004:i:3:p:671-676

DOI: 10.1016/j.physa.2004.06.050

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().