In some physical problems, the flux of material **M** has both a
diffusive
(down-gradient) component and a convective component (due to a velocity **v**)
in which
case the one dimensional flux can be expressed as

with **v** and allowed to depend on **x**, **t**, and **u** in general.
Use the conservation law, , **r = cu + b**, and the
above flux expression to derive the diffusion-convection conservation law PDE
.
In the case that **c**, **v**, and are constants, classify this PDE
as hyperbolic,
parabolic, or elliptic.