Diffusion Equation Set

$$\alpha$$$${\frac{{\partial \Phi}}{{\partial t}}}$$ - $$\mbox{$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{\nabla}$} \cdot$}$$D$$\mbox{$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{\nabla}$}$}$$$$\Phi$$ + $$\sigma$$$$\Phi$$ = S

Which can be written

$$\alpha$$$${\frac{{\partial \Phi}}{{\partial t}}}$$ + $$\mbox{$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{\nabla}$} \cdot$}$$$$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{F}$}$$ + $$\sigma$$$$\Phi$$ = S

$$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{F}$}$$ = - D$$\mbox{$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{\nabla}$}$}$$$$\Phi$$

Where

$$\Phi$$ = Intensity

$$\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{F}$}$$ = Flux

D = Diffusion Coefficient

$$\alpha$$ = Time Derivative Coefficient

$$\sigma$$ = Removal Coefficient

S = Intensity Source Term