Equations for nonlinear diffusion
Articles
Arvydas Juozapas Janavičius
Šiauliai university
Published 2010-12-21
https://doi.org/10.15388/LMR.2010.02
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Keywords

diffusion
diffusion coefficient
nonlinear diffusion equation
analytical solutions

How to Cite

Janavičius A. J. (2010) “Equations for nonlinear diffusion”, Lietuvos matematikos rinkinys, 51(proc. LMS), pp. 9–15. doi: 10.15388/LMR.2010.02.

Abstract

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.

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