Finite and infinite speed of propagation for porous medium equations with nonlocal pressure

Diana Stan, Félix del Teso, Juan Luis Vázquez

We study a porous medium equation with fractional potential pressure: $${\partial }_{t}u=\nabla \cdot (u^{m-1}\nabla p),p=(-\Delta {)}^{-s}u,$$ for $m>1$, $0<s<1$ and $u(x,t)\ge 0$.…