Conditions for the time global existence and nonexistence of a compact support of solutions to the Cauchy problem for quasilinear degenerate parabolic equations

We study a quasilinear degenerate parabolic equation with a nonhomogeneous density. We establish that depending on the behavior of the density at infinity either a solution to the Cauchy problem possesses the property that the speed of propagation of perturbations is finite or the support blows up in finite time.