The relativistic kinetic equations for two domains separated by a hypersurface with both spacelike and timelike parts are derived. The particle exchange between the domains separated by timelike boundaries generates source terms and modifies the collision term of the kinetic equation. The correct hydrodynamic equations for the “$\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{o}+\mathrm{\text{cascade}}$” models are obtained and their differences from existing freeze-out models of the hadronic matter are discussed.

• Received 20 November 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.252301