In Eq. 6, 
is a positive quantity
representing the flux of material
M in response to a unit gradient in the field variable u.
Time dependent conservation
law PDEs with flux ``down gradient'' are usually parabolic while steady
state conservation laws with such flux are generally elliptic.
These parabolic and elliptic conservation
law equations will be the vehicles by which a number of important
computational issues surrounding PDE problems will be introduced.
If we put the constitutive relationships Eq. 4 and
Eq. 6 into
the conservation law 
, the result is the one dimensional
parabolic conservation law PDE
where c denotes 
.
If density is a linear function of u,
and if 
is a constant, then Eq. 7 reduces to the constant
coefficient diffusion equation
where 
.
