Abstract: We study the general nonlinear diffusion equation ut=??(um?1?(??)?su) that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters m>1 and 01 by developing a new approximation method that allows one to treat the range m?3 , which could not be covered by previous works. We also extend the class of initial data to include any non-negative measure ? with finite mass. In passing from bounded initial data to measure data we make strong use of an L1- L? smoothing effect and other functional estimates. Finite speed of propagation is established for all m?2 , and this property implies the existence of free boundaries. The authors had already proved that finite propagation does not hold for m<2 .

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