...
Second order partial differential equation of parabolic type on the space-time field variable
:
| LaTeX Math Block |
|---|
|
\beta({\bf r}, U{\rm w}) \cdot \frac{\partial U {\rm w}}{\partial t} = \nabla \left( \alpha({\bf r}, U {\rm w}) \nabla U {\rm w} \right) + f({\bf r}) |
where
| space-time field variable | | LaTeX Math Inline |
|---|
| body | \alpha({\bf r}, U{\rm w}) |
|---|
|
| mobility kinetic coefficient |
|---|
| time | | LaTeX Math Inline |
|---|
| body | \beta({\bf r}, U{\rm w}) |
|---|
|
| capacitance kinetic coefficient |
|---|
| Position vector | | density of external forces |
|---|
...
| LaTeX Math Block |
|---|
|
\frac{\partial U {\rm w}}{\partial t} = D \cdot \Delta U {\rm w} |
where
is called the diffusion coefficient.
...
