Approximate analytical solutions of a nonlinear diffusion equation

Abstract

Approximate analytical solutions of a nonlinear diffusion equation $\frac{{\partial c}}{{\partial t}} = \frac{\partial }{{\partial x}}\left( {D(c)\frac{{\partial c}}{{\partial x}}} \right)$ are obtained in the practically important case of constant boundary conditions corresponding to the diffusion in a homogeneously doped half-space at a zero surface concentration for D(c) = ac, ac ², and a√c (a > 0). The error of approximation for these D(c) dependences in the concentration interval (1–2) × 10⁻³ < c < (0.92–0.99) does not exceed 1–2%.