{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/entropy-solutions-of-non-local-scalar","title":"Entropy solutions of non-local scalar conservation laws with congestion via deterministic particle method","arxiv_id":"2107.10760","date":"2021-07-22","proceeding":null,"authors":["Emanuela Radici","Federico Stra"],"abstract":"We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general assumptions that the existing literature: the velocity fields are less regular (in particular the interaction force can have a discontinuity at the origin) with no prescribed attractive/repulsive regime and the mobility can have unbounded support. We complement our results with some numerical simulations, among which we show the applicability of the schemes to the multi-species setting.","url_abs":"https://arxiv.org/abs/2107.10760v2","url_pdf":"https://arxiv.org/pdf/2107.10760v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"entropy-solutions-of-non-local-scalar","repo_url":"https://github.com/FedericoStra/ConservationLawsParticles.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"entropy-solutions-of-non-local-scalar","repo_url":"https://github.com/FedericoStra/cons-laws","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}