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research article

Approximate analytical solution of the nonlinear diffusion equation for arbitrary boundary conditions

Parlange, J.-Y.
•
Hogarth, W. L.
•
Parlange, M. B.  
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1998
Transport in Porous Media

A general approximation for the solution of the one- dimensional nonlinear diffusion equation is presented. It applies to arbitrary soil properties and boundary conditions. The approximation becomes more accurate when the soil-water diffusivity approaches a delta function, yet the result is still very accurate for constant diffusivity suggesting that the present formulation is a reliable one. Three examples are given where the method is applied, for a constant water content at the surface, when a saturated zone exists and for a time-dependent surface flux.

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