Abstract
The solutions of a coupled, linear and nonlinear diffusion equation in a semi-infinite medium are derived using series methods. In addition, perturbation techniques allied to the spectral decomposition of matrices are used to simplify the analysis and to find semianalytic solutions. The discussion is motivated by the transmission of heat, moisture, and solute through the strongly nonlinear medium of soil. Under boundary conditions representing the daily or seasonal fluctuations, it is shown using spectral decomposition, despite the nonlinearities, how the period of oscillation is preserved on passage through the medium. It is also shown how n 3 partial differential equations may be solved for each of the n coupled variables to determine closed forms for the first- and second-order perturbation effects. Examples of the solutions are given for the case of the coupled transport of heat and moisture in soil.
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