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.
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
First order hyperbolic conservation laws; Radon measure-valued solutions; entropy inequalities; 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].
Bertsch, M; Smarrazzo, F; Terracina, A; Tesei, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215054
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