We study the conditions under which the Cauchy problem for a linear hyperbolic system of partial differential equations of the first order in two independent variables has a unique continuous solution (not necessarily Lipschitz continuous). In addition to obvious continuity assumptions on coefficients and initial data, the sufficient conditions are the bounded variation of the left eigenvectors along the characteristic curves.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-3-5,
author = {Ma\l gorzata Zdanowicz and Zbigniew Peradzy\'nski},
title = {On continuous solutions to linear hyperbolic systems},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {273-281},
zbl = {1087.35527},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-3-5}
}
Małgorzata Zdanowicz; Zbigniew Peradzyński. On continuous solutions to linear hyperbolic systems. Annales Polonici Mathematici, Tome 85 (2005) pp. 273-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-3-5/