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Research Article | Open Access

Nonlocal scalar conservation laws with discontinuous flux

Felisia Angela Chiarello1( ), Giuseppe Maria Coclite2
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica (DISIM), University of L'Aquila, Via Vetoio, 67100 L'Aquila, Italy
Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Via E. Orabona 4, 70125 Bari, Italy
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Abstract

We prove the well-posedness of entropy weak solutions for a class of space-discontinuous scalar conservation laws with nonlocal flux. We approximate the problem adding a viscosity term and we provide L ∞ and BV estimates for the approximate solutions. We use the doubling of variable technique to prove the stability with respect to the initial data from the entropy condition.

Keywords

conservation lawsentropy solutionsdiscontinuous fluxnonlocal problem

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Networks and Heterogeneous Media
Volume 18 Issue 1,
March 2023
Pages 380-398
DOI: 10.3934/nhm.2023015

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Cite this article:
Chiarello FA, Coclite GM. Nonlocal scalar conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2023, 18(1): 380-398. https://doi.org/10.3934/nhm.2023015

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Received: 04 October 2022
Revised: 14 December 2022
Accepted: 19 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)