(  see Diffusion Equation @ Wikipedia )

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

\beta({\bf r}, U) \cdot \frac{\partial U}{\partial t} = \nabla \left(  \alpha({\bf r}, U)   \nabla U \right) +  f({\bf r}) 

where 

In the absence of external forces and constant kinetic coefficients the diffusion equation takes form:

\frac{\partial U}{\partial t} = D \Delta U +  f({\bf r}) 

where  is called the diffusion coefficient.