Nonlocal scalar conservation laws with discontinuous flux

Felisia Angela Chiarello; Giuseppe Maria Coclite; Felisia Angela Chiarello; Giuseppe Maria Coclite

doi:10.3934/nhm.2023015

Networks and Heterogeneous Media

2023, Volume 18, Issue 1: 380-398. doi: 10.3934/nhm.2023015

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Nonlocal scalar conservation laws with discontinuous flux

Felisia Angela Chiarello ^{1
,
,},
Giuseppe Maria Coclite ²

1.
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica (DISIM), University of L'Aquila, Via Vetoio, 67100 L'Aquila, Italy
2.
Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Via E. Orabona 4, 70125 Bari, Italy

Received: 04 October 2022 Revised: 14 December 2022 Accepted: 19 December 2022 Published: 29 December 2022

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 $ {{\bf{L}}^\infty} $ 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.
- conservation laws,
- entropy solutions,
- discontinuous flux,
- nonlocal problem
Citation: Felisia Angela Chiarello, Giuseppe Maria Coclite. Nonlocal scalar conservation laws with discontinuous flux[J]. Networks and Heterogeneous Media, 2023, 18(1): 380-398. doi: 10.3934/nhm.2023015

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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 $ {{\bf{L}}^\infty} $ 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.

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