  We introduce a notion of duality solution for a single or a system of
transport equations in spaces of probability measures reminiscent of the
viscosity solution notion for nonlinear parabolic equations. Our notion of
solution by duality is, under suitable assumptions, equivalent to gradient flow
solutions in case the single/system of equations has this structure. In
contrast, we can deal with a quite general system of nonlinear nonlocal,
diffusive or not, system of PDEs without any variational structure.
