Type: Article
Publication Date: 1993-04-01
Citations: 108
DOI: https://doi.org/10.1090/s0002-9939-1993-1120511-x
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 by 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.