@Article{CMAA-3-425,
author = {Ancona , FabioCaravenna , Laura and Marson , Andrea},
title = {SBV-Like Regularity of Entropy Solutions for a Scalar Balance Law},
journal = {Communications in Mathematical Analysis and Applications},
year = {2024},
volume = {3},
number = {3},
pages = {425--449},
abstract = {<p style="text-align: justify;">In this note, we demonstrate that solutions to scalar balance laws, in
one space dimension, which exhibit bounded variation, must be functions of
special bounded variation (SBV). This case study illustrates the strategy applied in [Ancona et al., preprint, University of Padova, 2024] to systems of
balance laws, extending the methodologies developed in pioneering previous
works by several authors. While for a single balance law a more general work
is already available, generalizing the first breakthrough related to a conservation law, the case of 1$D$ systems presents new behaviors that require a different strategy. This is why in this note we make the effort to introduce the
notation and tools that are required for the case of more equations. When the
flux presents linear degeneracies, it is known that entropy solutions can really
present nasty fractal Cantor-like behaviours, although $f
′
(u)$ is still SBV: We
thus discuss SBV-like regularity, as SBV-regularity fails.</p>},
issn = {2790-1939},
doi = {https://doi.org/10.4208/cmaa.2024-0018},
url = {http://global-sci.org/intro/article_detail/cmaa/23383.html}
}