English

Sharp a-contraction estimates for small extremal shocks

Analysis of PDEs 2023-11-23 v2

Abstract

In this paper, we study the aa-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 aa 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 2×22\times 2 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

R2 v1 2026-06-23T21:01:56.135Z