Hydrodynamic equation for a deposition model

We show that the two-component system of hyperbolic conservation laws $\partial_t \rho + \partial_x (\rho u) =0 = \partial_t u + \partial_x \rho$ appears naturally in the formally computed hydrodynamic limit of some randomly growing interface models, and we study some properties of this system. We show that the two-component system of hyperbolic conservation laws $\partial_t \rho + \partial_x (\rho u) =0 = \partial_t u + \partial_x \rho$ appears naturally in the formally computed hydrodynamic limit of some randomly growing interface models, and we study some properties of this system.