JournalsrlmVol. 30, No. 1pp. 137–168

A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws

  • Michiel Bertsch

    Università di Roma Tor Vergata, Italy

  • Flavia Smarrazzo

    Università Campus Bio-Medico di Roma, Italy

  • Andrea Terracina

    Università di Roma La Sapienza, Italy

  • Alberto Tesei

    Università di Roma La Sapienza, Italy
A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws cover

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Abstract

We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension, the initial data being a finite superposition of Dirac masses and the flux being Lipschitz continuous, bounded and sufficiently smooth. The novelty of the paper is the introduction of a compatibility condition which, combined with standard entropy conditions, guarantees uniqueness.

Cite this article

Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina, Alberto Tesei, A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 1, pp. 137–168

DOI 10.4171/RLM/839