Rigorous Estimates on Balance Laws in Bounded Domains
Analysis of PDEs
2015-04-09 v1
Abstract
The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in Bardos, Leroux and N\'ed\'elec (1979), striving to provide a rigorous treatment and detailed references.
Cite
@article{arxiv.1504.01907,
title = {Rigorous Estimates on Balance Laws in Bounded Domains},
author = {Rinaldo M. Colombo and Elena Rossi},
journal= {arXiv preprint arXiv:1504.01907},
year = {2015}
}