Open AccessEquations for nonlinear diffusion
Author(s) -
A.J. Janavičius
Publication year - 2010
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2010.02
Subject(s) - diffusion , brownian motion , anomalous diffusion , nonlinear system , diffusion equation , square root , impurity , effective diffusion coefficient , diffusion process , mathematical analysis , mathematics , physics , thermodynamics , innovation diffusion , geometry , statistics , quantum mechanics , medicine , knowledge management , economy , radiology , computer science , magnetic resonance imaging , economics , service (business)
The diffusion is the result of Brownian movement and occurs with a finite velocity. We presented the nonlinear diffusion equation, with diffusion coefficient directly proportional to the impurities concentration. Analytical solutions, showing that the maximum displacements of diffusing particles are proportional to the square root of diffusion time like for Brownian movement, was obtained. For small concentrations of impurities, nonlinear diffusion equation transforms to linear.