Abstract
A variational formulation is presented which has as its Euler-Lagrange equation the fundamental partial differential equation of diffusion. This variational expression is applicable for both time-dependent and time-independent boundary conditions and for a diffusion coefficient which is a function of the concentration. This variational technique is applied to the problem of unidimensional diffusion in a semi-infinite isotropic medium where the diffusion coefficient is strongly dependent upon the concentration of the diffuser. To solve the extremum problem, a system of “natural” finite difference equations is established as a consequence of the variational expression. Curves of concentration ratio vs distance are calculated and compared with a formal exact solution for a specific diffusion coefficient.
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