@article{3138ed091dff4636b8bb56967fcfad32,
title = "One-dimensional scalar conservation laws with regulated data",
abstract = "We show that the Kru{\v z}kov solution of the Cauchy problem for a scalar conservation law in one spatial dimension propagates regulated initial data into regulated solutions at later times. The proof is based on standard front-tracking and an extension, due to Fra{\v n}kov{\'a}, of Helly's selection principle. ",
author = "Jenssen, {Helge Kristian} and Johanna Ridder",
note = "Funding Information: \ast Received by the editors June 12, 2019; accepted for publication (in revised form) May 22, 2020; published electronically June 30, 2020. https://doi.org/10.1137/19M1267957 Funding: The work of the first author was partially supported by the National Science Foundation grant DMS-1813283. \dagger Department of Mathematics, Penn State University, University Park, State College, PA 16802 (hkjenssen@gmail.com, http://www.personal.psu.edu/hkj1/, johanna@jridder.de).",
year = "2020",
doi = "10.1137/19M1267957",
language = "English (US)",
volume = "52",
pages = "3114--3130",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}