Compactly Supported Evolution Vs Extinction for a special non-Newtonian diffusion

We discuss briefly the distinction of the phenomena of Finite propagation of speed and Extinction for scalar diffusion processes governed by non-Newtonian laws. First, we show that these two phenomena are well-distinguished for the classical p-Laplacian, and responsible for the underlying regularity theory. Then we introduce an anisotropic diffusion model, where the two phenomena are intertwined and cause loss of regularity.