Propagation of perturbation in a singular Cauchy problem for degenerate quasilinear parabolic equations

Cauchy problems for a wide class of 'doubly degenerate' divergent quasilinear parabolic equations of an arbitrary order are studied. This class contains, in particular, the equations of non-stationary Newtonian and non-Newtonian filtration. For arbitrary initial functions of the lowest local regularity acceptable from the viewpoint of the theory of solubility it is proved that the rate of evolution of the supports of the generalized solutions is finite. Upper estimates of this rate are obtained which are exact both for large and small times.