Abstract: One strategy for proving the global existence of admissible solutions to the Cauchy problem for first-order systems of conservation laws, is to introduce a small amount of diffusion and then pass to the limit. Under some structural assumption, this task was achived by DiPerna when the diffusion is given by artificial viscosity. We showed recently that this program works also for the Jin Xin relaxation. We prove here that it works well when the diffusion is given by a coupling with an elliptic equation. Such coupling arises in models for radiating gases.
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