...
LaTeX Math Block |
---|
|
\beta \cdot \frac{\partial {\rm w}}{\partial t} = \nabla \left( \alpha \nabla {\rm w} \right) + f({\bf r}) |
where
space-time field dynamic variable | LaTeX Math Inline |
---|
body | \alpha=\alpha({\bf r}, {\rm w}) |
---|
|
| mobility kinetic coefficient |
| time | LaTeX Math Inline |
---|
body | \beta=\beta({\bf r}, {\rm w}) |
---|
|
| capacitance kinetic coefficient |
---|
LaTeX Math Inline |
---|
body | {\bf r} = (x,y,z) \in R^3 |
---|
|
| position vector | | density of external forces |
---|
In the absence of external forces and constant kinetic coefficients the diffusion equation takes form:
...