We prove existence and uniqueness for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite superposition of Dirac masses, whereas the flux is Lipschitz continuous and bounded. The solution class is determined by an additional condition which is needed to prove uniqueness.

Bertsch, M., Smarrazzo, F., Terracina, A., Tesei, A. (2020). Signed radon measure-valued solutions of flux saturated scalar conservation laws. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 40(6), 3143-3169 [10.3934/dcds.2020041].

Signed radon measure-valued solutions of flux saturated scalar conservation laws

Bertsch M.;
2020-01-01

Abstract

We prove existence and uniqueness for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite superposition of Dirac masses, whereas the flux is Lipschitz continuous and bounded. The solution class is determined by an additional condition which is needed to prove uniqueness.
2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
First order hyperbolic conservation laws; signed Radon measures; singular boundary conditions; entropy inequalities; uniqueness
Bertsch, M., Smarrazzo, F., Terracina, A., Tesei, A. (2020). Signed radon measure-valued solutions of flux saturated scalar conservation laws. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 40(6), 3143-3169 [10.3934/dcds.2020041].
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/2108/244290
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