A front-tracking alternative to the random choice method. (English) Zbl 0799.35153

Summary: An alternative to Glimm’s proof of the existence of solutions to systems of hyperbolic conservation laws is presented. The proof is based on an idea of Dafermos for the single conservation law and in some respects simplifies Glimm’s original argument. The proof is based on construction of approximate solutions of which a subsequence converges. It is shown that the constructed solution satisfies Lax’s entropy inequalities. The construction also gives a numerical method for solving such systems.


35L65 Hyperbolic conservation laws
35D05 Existence of generalized solutions of PDE (MSC2000)
76T99 Multiphase and multicomponent flows
35L67 Shocks and singularities for hyperbolic equations
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