--- res: bibo_abstract: - The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Klemens foaf_name: Fellner, Klemens foaf_surname: Fellner - foaf_Person: foaf_givenName: Julian L foaf_name: Fischer, Julian L foaf_surname: Fischer foaf_workInfoHomepage: http://www.librecat.org/personId=2C12A0B0-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-0479-558X - foaf_Person: foaf_givenName: Michael foaf_name: Kniely, Michael foaf_surname: Kniely foaf_workInfoHomepage: http://www.librecat.org/personId=2CA2C08C-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5645-4333 - foaf_Person: foaf_givenName: Bao Quoc foaf_name: Tang, Bao Quoc foaf_surname: Tang bibo_doi: 10.1007/s00332-023-09926-w bibo_volume: 33 dct_date: 2023^xs_gYear dct_identifier: - UT:001002343400002 dct_isPartOf: - http://id.crossref.org/issn/0938-8974 - http://id.crossref.org/issn/1432-1467 dct_language: eng dct_publisher: Springer Nature@ dct_title: Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion@ ...