  We illustrate an alternative derivation of the viscous regularization of the
diffusion equation which was studied in [A. Novick-Cohen and R. L. Pego. {\em
Trans. Amer. Math. Soc.}, 324:331--351]. We provide an alternative proof of
existence of solutions, based on the Galerkin method and on compactness
arguments. In addition, we propose a "non-smooth" variant of the viscous
regularization which we believe may result in interesting hysteretic effects.
