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Second order partial differential equation of parabolic type on the space-time field variable  {\rm w}(t, {\bf r}):

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


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

dynamic variable

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

mobility kinetic coefficient



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

capacitance kinetic coefficient

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

position vector

f({\bf r})

density of external forces

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

(2) \frac{\partial {\rm w}}{\partial t} = D \cdot \Delta {\rm w}

where  D is called diffusion coefficient:

(3) D = \frac{M}{\beta}

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