SOME NONLINEAR DIFFUSION-EQUATIONS AND FRACTAL DIFFUSION

Authors
Citation
J. Stephenson, SOME NONLINEAR DIFFUSION-EQUATIONS AND FRACTAL DIFFUSION, Physica. A, 222(1-4), 1995, pp. 234-247
Citations number
9
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
ISSN journal
0378-4371
Volume
222
Issue
1-4
Year of publication
1995
Pages
234 - 247
Database
ISI
SICI code
0378-4371(1995)222:1-4<234:SNDAFD>2.0.ZU;2-6
Abstract
Some scaling solutions of a class of radially symmetric non-linear dif fusion equations in an arbitrary dimension d are obtained, (A) for an initial point source with a fixed total amount of material, and (B) fo r a radial flux of material through a hyper-spherical surface. In this macroscopic model the flux density depends on powers of the concentra tion and its (radial) gradient. The dimensional dependence of these so lutions is analyzed and comparison made with scaling solutions of the corresponding linear equations for fractal diffusion. The non-linear e quations contain arbitrary exponents which can be related to an effect ive fractal dimension of the underlying diffusion process.