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.
Bertsch, M., Smarrazzo, F., Terracina, A., Tesei, A. (2019). A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws,. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 30(1), 137-168 [10.4171/RLM/839].
A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws,
Bertsch M.
;Tesei A.
2019-01-01
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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