{"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/an-entropy-structure-preserving-space-time","title":"An entropy structure preserving space-time formulation for cross-diffusion systems: Analysis and Galerkin discretization","arxiv_id":"2006.13069","date":"2020-06-23","proceeding":null,"authors":["Marcel Braukhoff","Ilaria Perugia","Paul Stocker"],"abstract":"Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and cell biology. We present a space-time approach to the proof of existence of bounded weak solutions of cross-diffusion systems, making use of the system entropy to examine long-term behavior and to show that the solution is nonnegative, even when a maximum principle is not available. This approach naturally gives rise to a novel space-time Galerkin method for the numerical approximation of cross-diffusion systems that conserves their entropy structure. We prove existence and convergence of the discrete solutions, and present numerical results for the porous medium, the Fisher-KPP, and the Maxwell-Stefan problem.","url_abs":"https://arxiv.org/abs/2006.13069v2","url_pdf":"https://arxiv.org/pdf/2006.13069v2.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":"an-entropy-structure-preserving-space-time","repo_url":"https://github.com/paulst/crossdiff","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}