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

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

dynamic variable

LaTeX Math Inline
body\alphaM=\alphaM({\bf r}, {\rm w})

mobility kinetic coefficient

LaTeX Math Inline
body{t}

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

LaTeX Math Inline
body f({\bf r})

density of external forces

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where 

LaTeX Math Inline
bodyD
 is called the diffusion coefficient.:

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D = \frac{M}{\beta}