( see Diffusion Equation @ Wikipedia )@wikipedia
Second order partial differential equation of parabolic type on the space-time field variable
:
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\beta({\bf r}, U) \cdot \frac{\partial U{\rm w}}{\partial t} = \nabla \left( M \alpha(nabla {\bfrm r}, U) \nabla Uw} \right) + f({\bf r}) |
where
Uspace-time field | t | time | mobility kinetic coefficient |
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\bf r} = (x,y,z)Position vector f| \beta=\beta({\bf r}, {\rm w}) |
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density of external forcescapacitance kinetic coefficient |
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\alpha( Umobility kinetic coefficient\beta, Ucapacitance kinetic coefficient| density of external forces |
In the absence of external forces and constant kinetic coefficients the diffusion equation takes Diffusion Equation takes form:
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\frac{\partial U{\rm w}}{\partial t} = D \cdot \Delta U + f({\bfrm rw}) |
where
is called
the diffusion coefficient.:| LaTeX Math Block |
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D = \frac{M}{\beta} |
