Hyperbolic phenomena in a strongly degenerate parabolic equation

We consider the equation u_t=((u) (u_x))_x, where >0 and where is a strictly increasing function with lim_s=<. We solve the associated Cauchy problem for an increasing initial function, and discuss to what extent the solution behaves qualitatively like solutions of the first-order conservation law u_t=((u))_x. Equations of this type arise, for example, in the theory of phase transitions where the corresponding free-energy functional has a linear growth rate with respect to the gradient.