On some general properties of parabolic conservation equations

This report deals with certain general properties of partial differential equations of the form S(c)ct + qz = Q(c), where t may thought of as time, z as distance, c as an intensive quantity (e.g., temperature), and q its flux (e.g., heat flux), and where q depends on both c and cz. Six topics are studied, namely: Maximum and minimum principles; ordering of solutions; invariance to stretching (affine) groups; stability of steady states; comparability of solutions; and traveling wave solutions. Illustrative examples are given from the field of nonlinear diffusion, applied superconductivity, and helium cryogenics