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Updated: Aug 19, 2025

Evolution of Staircase Structures in Diffusive Convection
Published on: September 5, 2018
Derivation and analytical solutions of a non-linear diffusion equation applied to non-constant heat conductivity and
1Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile.
Abstract:
This paper derives a non-linear diffusion equation discussing two possible applications: the ionic diffusion in glasses and temperature-dependent conductivity in semiconductors. The first equation is a logarithmic diffusion derived formally from the continuity of ion concentration, but the latter is a more phenomenological example. A power-law ansatz with time-dependent parameters maximizes a non-standard entropy and gives a set of coupled motion equations we can solve analytically. These results build the general solution to the non-linear diffusion equation.
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