Method for the Exact Solution of a Nonlinear Diffusion-Convection Equation

For a prescribed adsorption-desorption equilibrium maintained locally through a permeable solid, the concentration of a chemical substance is governed by the diffusionconvection equation $\frac{\partial c}{\partial t}=(D{\nabla }^2-\overrightarrow{\mathrm{v}}·\nabla )\left[\frac{c}{(1+K^{-1\mathrm{}}c)}\right]$ in which $\frac{c}{(1+K^{-1\mathrm{}}c)}$ is the free concentration of the substance. Solutions of this nonlinear equation are shown to be related analytically to solutions of the elementary linear diffusion equation. This remarkable correspondence is utilized to obtain exact solutions to the nonlinear diffusionconvection equation.