Abstract

We consider the space of solutions to the continuity equation $d/dt~u(t,x) + div~j(t,x) = 0$ equipped with convex action functionals $A(u,j)$, which encode microstructure in e.g. porous media or road networks. In the limit over long distances, we compute the effective transport cost in terms of Gamma-convergence, with applications to the porous media equation.