{"date_created":"2023-06-18T22:00:45Z","author":[{"orcid":"0000-0002-9573-2962","last_name":"Agresti","full_name":"Agresti, Antonio","first_name":"Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"last_name":"Veraar","full_name":"Veraar, Mark","first_name":"Mark"}],"citation":{"apa":"Agresti, A., &#38; Veraar, M. (2023). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. <i>Journal of Differential Equations</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">https://doi.org/10.1016/j.jde.2023.05.038</a>","ista":"Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 368(9), 247–300.","short":"A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.","mla":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” <i>Journal of Differential Equations</i>, vol. 368, no. 9, Elsevier, 2023, pp. 247–300, doi:<a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">10.1016/j.jde.2023.05.038</a>.","ama":"Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. <i>Journal of Differential Equations</i>. 2023;368(9):247-300. doi:<a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">10.1016/j.jde.2023.05.038</a>","ieee":"A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity,” <i>Journal of Differential Equations</i>, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.","chicago":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” <i>Journal of Differential Equations</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">https://doi.org/10.1016/j.jde.2023.05.038</a>."},"publication_identifier":{"issn":["0022-0396"],"eissn":["1090-2732"]},"publication":"Journal of Differential Equations","_id":"13135","publication_status":"published","doi":"10.1016/j.jde.2023.05.038","issue":"9","tmp":{"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)","image":"/images/cc_by.png"},"date_updated":"2024-01-29T11:04:41Z","file_date_updated":"2024-01-29T11:03:09Z","day":"25","acknowledgement":"The first author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 948819) Image 1. The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","scopus_import":"1","publisher":"Elsevier","type":"journal_article","title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity","date_published":"2023-09-25T00:00:00Z","has_accepted_license":"1","month":"09","oa":1,"article_processing_charge":"Yes (in subscription journal)","isi":1,"intvolume":"       368","file":[{"file_size":834638,"success":1,"checksum":"246b703b091dfe047bfc79abf0891a63","file_name":"2023_JourDifferentialEquations_Agresti.pdf","content_type":"application/pdf","creator":"dernst","relation":"main_file","date_created":"2024-01-29T11:03:09Z","access_level":"open_access","date_updated":"2024-01-29T11:03:09Z","file_id":"14895"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"year":"2023","status":"public","quality_controlled":"1","article_type":"original","license":"https://creativecommons.org/licenses/by/4.0/","ddc":["510"],"page":"247-300","language":[{"iso":"eng"}],"department":[{"_id":"JuFi"}],"external_id":{"isi":["001019018700001"]},"oa_version":"Published Version","volume":368,"abstract":[{"lang":"eng","text":"In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model."}],"project":[{"name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","call_identifier":"H2020"}]}