Nonlinear diffusivity dependence on dimensions
Arvydas Juozapas Janavičius
Šiauliai University
Sigita Turskienė
Šiauliai University
Kęstutis Žilinskas
Šiauliai University
Published 2015-12-15


nonlinear diffusion equation
diffusion coefficients in higher dimensional
approximate analytical solution

How to Cite

Janavičius A. J., Turskienė S. and Žilinskas K. (2015) “Nonlinear diffusivity dependence on dimensions”, Lietuvos matematikos rinkinys, 56(A), pp. 24–29. doi: 10.15388/LMR.A.2015.05.


The nonlinear diffusion equation corresponds to the diffusion processes which can occur with a finite velocity. This statement is not satisfied in Fick’s second law or linear diffusion equation. The processes by which different materials mix in the result of the random Brownian motions of atoms, molecules and ions can be exactly described only with presented nonlinear equation. It was important in practice that theoretically profiles fit with the experimental profiles tail region, but get good coincidence between diffusion experiments and the classical solutions is impossible. By using obtained theoretical solutions for two and three-dimensional cases we can provide more exact modeling of all the stages of a planar transistor formation.

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