Augustus: Diffusion (P1 ) Equation Set

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

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

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

$\displaystyle \Phi$	=	Intensity
$\displaystyle \mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{F}$}$	=	Flux
D	=	Diffusion Coefficient
$\displaystyle \alpha$	=	Time Derivative Coefficient
$\displaystyle \sigma$	=	Removal Coefficient
S	=	Intensity Source Term
$\displaystyle \mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{J}$}$	=	Flux Source Term