{"status":"public","title":"Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion","quality_controlled":"1","scopus_import":"1","publisher":"Springer Nature","date_created":"2021-12-16T12:15:35Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","oa":1,"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."}],"department":[{"_id":"JuFi"}],"publication_status":"published","date_published":"2023-06-07T00:00:00Z","date_updated":"2023-08-01T14:40:33Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"06","article_processing_charge":"No","day":"07","type":"journal_article","file":[{"file_name":"2023_JourNonlinearScience_Fellner.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","relation":"main_file","checksum":"f3f0f0886098e31c81116cff8183750b","file_size":742315,"date_created":"2023-06-19T07:33:53Z","file_id":"13149","success":1,"date_updated":"2023-06-19T07:33:53Z"}],"ddc":["510"],"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.","isi":1,"file_date_updated":"2023-06-19T07:33:53Z","year":"2023","volume":33,"intvolume":"        33","_id":"10550","article_number":"66","language":[{"iso":"eng"}],"citation":{"ama":"Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. <i>Journal of Nonlinear Science</i>. 2023;33. doi:<a href=\"https://doi.org/10.1007/s00332-023-09926-w\">10.1007/s00332-023-09926-w</a>","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.” <i>Journal of Nonlinear Science</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00332-023-09926-w\">https://doi.org/10.1007/s00332-023-09926-w</a>.","apa":"Fellner, K., Fischer, J. L., Kniely, M., &#38; Tang, B. Q. (2023). Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. <i>Journal of Nonlinear Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00332-023-09926-w\">https://doi.org/10.1007/s00332-023-09926-w</a>","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.","short":"K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023).","mla":"Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” <i>Journal of Nonlinear Science</i>, vol. 33, 66, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00332-023-09926-w\">10.1007/s00332-023-09926-w</a>.","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,” <i>Journal of Nonlinear Science</i>, vol. 33. Springer Nature, 2023."},"article_type":"original","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"external_id":{"isi":["001002343400002"],"arxiv":["2109.12019"]},"publication":"Journal of Nonlinear Science","has_accepted_license":"1","author":[{"full_name":"Fellner, Klemens","first_name":"Klemens","last_name":"Fellner"},{"first_name":"Julian L","last_name":"Fischer","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X"},{"orcid":"0000-0001-5645-4333","full_name":"Kniely, Michael","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","last_name":"Kniely","first_name":"Michael"},{"full_name":"Tang, Bao Quoc","first_name":"Bao Quoc","last_name":"Tang"}],"doi":"10.1007/s00332-023-09926-w"}