Second order partial differential equation of parabolic type on the space-time field variable {\rm w}(t, {\bf r}):
| (1) | \beta \cdot \frac{\partial {\rm w}}{\partial t} = \nabla \left( M \nabla {\rm w} \right) + f({\bf r}) |
where
{\rm w}(t, {\bf r}) | dynamic variable | M=M({\bf r}, {\rm w}) | mobility kinetic coefficient |
|---|---|---|---|
{t} | time | \beta=\beta({\bf r}, {\rm w}) | capacitance kinetic coefficient |
{\bf r} = (x,y,z) \in R^3 | position vector | f({\bf r}) | density of external forces |
In the absence of external forces and constant kinetic coefficients the Diffusion Equation takes form:
| (2) | \frac{\partial {\rm w}}{\partial t} = D \cdot \Delta {\rm w} |
where D is called diffusion coefficient:
| (3) | D = \frac{M}{\beta} |