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