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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 \alpha U | mobility kinetic coefficient |
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U | capacitance kinetic coefficient |
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| body | {\bf r} = (x,y,z) \in R^3 |
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Position
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 {\rm w} |
where
is called
the diffusion coefficient.:| LaTeX Math Block |
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D = \frac{M}{\beta} |
