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Existence of solutions to hyperbolic conservation laws with a source. (English) Zbl 0883.35074
The Cauchy problem for an extended model of isothermal flow as well as two related systems is considered. Each system describes a physically relevant flow and existence proofs are given for all three models. Although the three proofs turn out to be quite different, the unifying theme is a vanishing viscosity Ansatz in conjunction with compensated compactness techniques. Corresponding entropy-entropy flux pairs are constructed.

MSC:
35L65Conservation laws
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