Diffusion in Nonlinear Multiplicative Media

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Abstract
The time‐dependent behavior of the nonlinear distributions defined by the diffusion equation with several nonlinear source terms is studied. The nonlinear diffusion equation is solved by an eigenfunction‐expansion method, which is in principle independent of geometry or number of dimensions. The qualitative time behavior of the distributions and their steady states can be ascertained from a simple analysis of the fundamental mode approximation only. Explicit solutions are presented in one‐ and two‐dimensional geometries.

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