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.
A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws / Bertsch, Michiel; Smarrazzo, Flavia; Terracina, Andrea; Tesei, Alberto. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 30:1(2019), pp. 137-168. [10.4171/RLM/839]
A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws
Terracina, Andrea;Tesei, Alberto
2019
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.| File | Dimensione | Formato | |
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