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Research Article | Open Access

An Oleinik inequality for a class of heterogeneous balance laws

Rida Harb, Stéphane Junca( )
Université Côte d'Azur, LJAD, Parc Valrose, F-06108 Nice, France
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Abstract

Although an Oleinik inequality is not expected for general heterogeneous scalar balance laws, there is a favorable case, when the source term g ( x ) is smooth and nondecreasing. In this setting, we are able to obtain an Oleinik-type inequality and, consequently, a smoothing effect.

Keywords

balance lawsentropy solutionstrictly convex fluxOleinik inequalitywave interactiongeneralized Riemann problemregularizing effect

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Networks and Heterogeneous Media
Volume 21 Issue 1,
March 2026
Pages 22-54
DOI: 10.3934/nhm.2026002

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Harb R, Junca S. An Oleinik inequality for a class of heterogeneous balance laws. Networks and Heterogeneous Media, 2026, 21(1): 22-54. https://doi.org/10.3934/nhm.2026002

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Received: 05 November 2025
Revised: 28 December 2025
Accepted: 05 January 2026
Published: 15 March 2026
©2026 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)