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An informal account of recent results on initial-boundary value problems for systems of conservation laws

Analysis of PDEs 2024-05-06 v1

Abstract

This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear systems of conservation laws defined in domains with boundaries. The main novelty in [4] is that the solution is constructed by taking into account the underlying viscous mechanism, which is relevant because, in the case of initial-boundary value problems, different viscous approximations yield in general different limits. This note will frame the analysis of [4] in the relevant context, compare the main result with the previous existing literature, and touch upon the most innnovative technical points of the proof.

Keywords

Cite

@article{arxiv.2405.02096,
  title  = {An informal account of recent results on initial-boundary value problems for systems of conservation laws},
  author = {Laura V. Spinolo and Fabio Ancona and Andrea Marson},
  journal= {arXiv preprint arXiv:2405.02096},
  year   = {2024}
}

Comments

Dedicated to Professor Gui-Qiang Chen on the occasion of his 60th birthday