--- _id: '10550' abstract: - lang: eng text: 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. acknowledgement: "We thank the referees for their valuable comments and suggestions. A major part of this work was carried out when B. Q. Tang visited the Institute of Science and Technology Austria (ISTA). The hospitality of ISTA is greatly acknowledged. This work was partially supported by NAWI Graz.\r\nOpen access funding provided by University of Graz." article_number: '66' article_processing_charge: No article_type: original author: - first_name: Klemens full_name: Fellner, Klemens last_name: Fellner - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 - first_name: Bao Quoc full_name: Tang, Bao Quoc last_name: Tang citation: ama: Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-023-09926-w apa: Fellner, K., Fischer, J. L., Kniely, M., & Tang, B. Q. (2023). Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-09926-w chicago: Fellner, Klemens, Julian L Fischer, Michael Kniely, and Bao Quoc Tang. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science. Springer Nature, 2023. https://doi.org/10.1007/s00332-023-09926-w. ieee: K. Fellner, J. L. Fischer, M. Kniely, and B. Q. Tang, “Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion,” Journal of Nonlinear Science, vol. 33. Springer Nature, 2023. ista: Fellner K, Fischer JL, Kniely M, Tang BQ. 2023. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 33, 66. mla: Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science, vol. 33, 66, Springer Nature, 2023, doi:10.1007/s00332-023-09926-w. short: K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023). date_created: 2021-12-16T12:15:35Z date_published: 2023-06-07T00:00:00Z date_updated: 2023-08-01T14:40:33Z day: '07' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00332-023-09926-w external_id: arxiv: - '2109.12019' isi: - '001002343400002' file: - access_level: open_access checksum: f3f0f0886098e31c81116cff8183750b content_type: application/pdf creator: dernst date_created: 2023-06-19T07:33:53Z date_updated: 2023-06-19T07:33:53Z file_id: '13149' file_name: 2023_JourNonlinearScience_Fellner.pdf file_size: 742315 relation: main_file success: 1 file_date_updated: 2023-06-19T07:33:53Z has_accepted_license: '1' intvolume: ' 33' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version publication: Journal of Nonlinear Science publication_identifier: eissn: - 1432-1467 issn: - 0938-8974 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 33 year: '2023' ...