Existence of weak solutions for a general porous medium equation with nonlocal pressure

Diana Stan, Félix del Teso, Juan Luis Vázquez

We study the general nonlinear diffusion equation $u_t=\nabla \cdot (u^{m-1}\nabla (-\Delta {)}^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure.…