@article{0971edc5e751418d9db30bec168156e6,
title = "EXAMPLES AND CONJECTURES ON THE REGULARITY OF SOLUTIONS TO BALANCE LAWS",
abstract = "The paper discusses various regularity properties for solutions to a scalar, 1-dimensional conservation law with strictly convex flux and integrable source. In turn, these yield compactness estimates on the solution set. Similar properties are expected to hold for 2 × 2 genuinely nonlinear systems.",
author = "Fabio Ancona and Stefano Bianchini and Alberto Bressan and Colombo, {Rinaldo M.} and Nguyen, {Khai T.}",
note = "Funding Information: Received November 13, 2022. 2020 Mathematics Subject Classification. Primary 35L65, 35L67; Secondary 35L40. The research of the first author was partially supported by the Istituto Nazionale di Alta Matematica {\textquoteright}F. Severi{\textquoteright}, through GNAMPA. The research of the third author was partially supported by NSF with grant DMS-2006884 “Singularities and error bounds for hyperbolic equations”. The research of the fifth author was partially supported by NSF with grant DMS-2154201 “Generic Singularities and Fine Regularity Structure for Nonlinear Partial Differential Equations”. F. Ancona, S. Bianchini, R. M. Colombo and K. T. Nguyen acknowledge the hospitality of Penn State University, where the collaboration leading to this work took place. Email address: ancona@math.unipd.it Email address: bianchin@sissa.it Email address: axb62@psu.edu Email address: rinaldo.colombo@unibs.it Email address: khai@math.ncsu.edu Publisher Copyright: {\textcopyright} 2023 Brown University",
year = "2023",
doi = "10.1090/qam/1647",
language = "English (US)",
volume = "81",
pages = "433--454",
journal = "Quarterly of Applied Mathematics",
issn = "0033-569X",
publisher = "American Mathematical Society",
number = "3",
}