Propagation of perturbations in processes described by degenerate parabolic equations with nonpower nonlinearities

The paper deals with the homogeneous first boundary-value problem for a one-dimensional quasilinear second-order parabolic equation without any assumptions about the nonlinear solution functions and their derivatives to be of power type. A criterion for the finiteness of the velocity of the propagation of perturbations is found. The influence of the zero order of the initial function at an inner point on the evolution of the corresponding component of the solution support is investigated.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 10, pp. 118–134, 1984.