@article{Harb2026, 
author = {Rida Harb and Stéphane Junca},
title = {An Oleinik inequality for a class of heterogeneous balance laws},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {1},
pages = {22-54},
keywords = {balance laws, entropy solution, strictly convex flux, Oleinik inequality, wave interaction, generalized Riemann problem, regularizing effect},
url = {https://www.sciopen.com/article/10.3934/nhm.2026002},
doi = {10.3934/nhm.2026002},
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.}
}