  Based on the conservation-dissipation formalism proposed by Zhu and
collaborators we formulate a general version of the Israel-Stewart theory for
relativistic fluid dynamics with bulk viscosity. Our generalization consists in
allowing for a wide range of dependence of the entropy density on the bulk
viscosity. We show the existence of Godunov-Boillat variables for this model.
By known properties of systems possessing such variables, this provides an
alternative proof of the recently established existence of solutions for the
Israel-Stewart theory locally in time, and a proof that entropy production is
positive across weak Lax shocks.
