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

Michiel Bertsch; Flavia Smarrazzo; Andrea Terracina; Alberto Tesei

doi:10.3934/dcds.2020041

Article Contents

2020, Volume 40, Issue 6: 3143-3169. Doi: 10.3934/dcds.2020041 open access

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

1.
Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy, and, Istituto per le Applicazioni del Calcolo "M. Picone", CNR, Roma, Italy
2.
Facoltà Dipartimentale di Ingegneria, Università Campus Bio-Medico di Roma, Via Alvaro del Portillo 21, 00128 Roma, Italy
3.
Dipartimento di Matematica "G. Castelnuovo", Università "Sapienza" di Roma, P.le A. Moro 5, I-00185 Roma, Italy
4.
Istituto per le Applicazioni del Calcolo "M. Picone", CNR, Roma, Italy

^* Corresponding author: Alberto Tesei
^* Corresponding author: Alberto Tesei

Received: January 31, 2019

Published: March 2020

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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.

Keywords:

First order hyperbolic conservation laws,
signed Radon measures,
singular boundary conditions,
entropy inequalities,
uniqueness.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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