Sufficient and necessary conditions for the existence and uniqueness of classical solutions to the Cauchy problem for the scalar conservation law are found in the class of discontinuous initial data and non-convex flux function. Regularity of rarefaction waves starting from discontinuous initial data and their dependence on the flux function are investigated and illustrated in a few examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-1,
author = {J\k edrzej Jab\l o\'nski},
title = {Classical solutions to the scalar conservation law with discontinuous initial data},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {1-12},
zbl = {1277.35250},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-1}
}
Jędrzej Jabłoński. Classical solutions to the scalar conservation law with discontinuous initial data. Colloquium Mathematicae, Tome 131 (2013) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-1/