We first recall the concept of hydrodynamical equation of an infinite particle system. We then prove that the equation associated to the zero-range process is a first order nonlinear partial differential equation.
Enrique D. Andjel. Claude Kipnis. "Derivation of the Hydrodynamical Equation for the Zero-Range Interaction Process." Ann. Probab. 12 (2) 325 - 334, May, 1984. https://doi.org/10.1214/aop/1176993293