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