An Oleinik inequality for a class of heterogeneous balance laws

Networks and Heterogeneous Media 2026 Open access

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Authors: Rida Harb, Université Côte d'Azur, LJAD, Parc Valrose, F-06108 Nice, France, Stéphane Junca
DOI: 10.3934/nhm.2026002
Cited by: 1
References: 25

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.

Fields of Study & Subjects

Stability and Controllability of Differential Equations Nonlinear Differential Equations Analysis Navier-Stokes equation solutions

Publication details

Journal / source
Networks and Heterogeneous Media
Publisher
American Institute of Mathematical Sciences (AIMS)
Volume
21
Issue
1
Pages
22–54
Publication date
1 January 2026
Language
EN