A remark on duality solutions for some weakly nonlinear scalar conservation laws
Analysis of PDEs
2011-06-27 v1
Abstract
We investigate existence and uniqueness of duality solutions for a scalar conservation law with a nonlocal interaction kernel. Following the work of Bouchut and James (Comm. Partial Diff. Eq., 24, 1999), a notion of duality solution for such a nonlinear system is proposed, for which we do not have uniqueness. Then we prove that a natural definition of the flux allows to select a solution for which uniqueness holds.
Cite
@article{arxiv.1105.1308,
title = {A remark on duality solutions for some weakly nonlinear scalar conservation laws},
author = {François James and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:1105.1308},
year = {2011}
}