**Papers Published**

- with Bryant, RL; Griffiths, PA,
*Characteristic cohomology of differential systems, II: Conservation laws for a class of parabolic equations*, Duke Math. Journal, vol. 78 no. 3 (1995), pp. 531-676

(last updated on 2018/07/22)**Author's Comments:**

In this long paper, we apply the ideas from Part I together with the equivalence method to classify the parabolic PDE in the plane that admit conservation laws. We show, in particular, that a parabolic PDE that has more than 3 independent conservation laws is linearizable by a (contact) change of coordinates and exhibit equations (to our knowledge, the first known ones) of parabolic equations that have exactly 3 independent conservation laws. In the final section of the paper, we prove a classification theorem for parabolic systems that admit non-trivial integrable extensions (i.e., 'coverings' in Vinogradov's terminology) and give examples of systems that admit non-trivial coverings but no conservation laws.My former student, Jeanne Nielsen Clelland (now at the University of Colorado in Boulder), has now generalized many of these results to the case of two independent space variables and is developing the theory very nicely.