Nonlocal scalar conservation laws with discontinuous flux

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 variabl...

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Veröffentlicht in:Networks and heterogeneous media 2023-01, Vol.18 (1), p.380-398
Hauptverfasser: Chiarello, Felisia Angela, Coclite, Giuseppe Maria
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1556-1801
DOI:10.3934/nhm.2023015