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General hyperbolic systems of balance laws with inhomogeneous flux and sourceare studied. Global existence of entropy weak solutions to the Cauchy problemis established for small $BV$ data under appropriate assumptions on the decayof the flux and the source with respect to space and time. There is neither ahypothesis about equilibrium solution nor about the dependence of the source onthe state vector as previous results have assumed.

A remark on the Glimm scheme for inhomogeneous hyperbolic systems of balance laws