Sharp a-contraction estimates for small extremal shocks
Analysis of PDEs
2023-11-23 v2
Abstract
In this paper, we study the -contraction property of small extremal shocks for 1-d systems of hyperbolic conservation laws endowed with a single convex entropy, when subjected to large perturbations. We show that the weight coefficient can be chosen with amplitude proportional to the size of the shock. The main result of this paper is a key building block in the companion paper, [{arXiv:2010.04761}, 2020], in which uniqueness and BV-weak stability results for systems of hyperbolic conservation laws are proved.
Keywords
Cite
@article{arxiv.2012.09261,
title = {Sharp a-contraction estimates for small extremal shocks},
author = {William Golding and Sam Krupa and Alexis Vasseur},
journal= {arXiv preprint arXiv:2012.09261},
year = {2023}
}
Comments
41 pages, 2 figures, minor correction to lemma 4.2 and corresponding changes to section 4