A quasilinear parabolic equation with inhomogeneous density and absorption

We deal with the initial-boundary value problem for a quasilinear degenerate parabolic equation with inhomogeneous density and absorption, which appears in a number of applications to describe the evolution of diffusion processes, in particular non-Newtonian flow in a porous medium. We discuss the extinction of solution and the finite speed of propagation of perturbations