  General hyperbolic systems of balance laws with inhomogeneity in space and
time in all constitutive functions are studied in the context of relative
entropy. A framework is developed in this setting that contributes to a
measure-valued weak vs strong uniqueness theorem, a stability theorem of
viscous solutions and a convergence theorem as the viscosity parameter tends to
zero. The main goal of this paper is to develop hypotheses under which the
relative entropy framework can still be applied. Examples of systems with
inhomogeneity that have different charateristics are presented and the
hypotheses are discussed in the setting of each example.
