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@wikipedia

Second order partial differential equation of parabolic type on the space-time field variable

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body {\rm w}(t, {\bf r})
:

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anchor 1 left
\beta \cdot \frac{\partial {\rm w}}{\partial t} = \nabla \left(  M  \nabla {\rm w} \right) +  f({\bf r})

where

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body {\rm w}(t, {\bf r})

dynamic variable

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body M=M({\bf r}, {\rm w})

mobility kinetic coefficient

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body {t}

time

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body \beta=\beta({\bf r}, {\rm w})

capacitance kinetic coefficient

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body {\bf r} = (x,y,z) \in R^3

position vector

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body f({\bf r})

density of external forces

In the absence of external forces and constant kinetic coefficients the Diffusion Equation takes form:

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anchor R8SB3 left
\frac{\partial {\rm w}}{\partial t} = D \cdot \Delta {\rm w}

where

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body D
is called diffusion coefficient:

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anchor D left
D = \frac{M}{\beta}