{"month":"12","date_created":"2021-01-24T23:01:09Z","abstract":[{"lang":"eng","text":"We give a short and self-contained proof for rates of convergence of the Allen--Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen--Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems."}],"ec_funded":1,"ddc":["510"],"publication_identifier":{"eissn":["10957154"],"issn":["00361410"]},"oa":1,"date_updated":"2023-08-24T11:15:16Z","title":"Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000600695200027"]},"publication":"SIAM Journal on Mathematical Analysis","author":[{"orcid":"0000-0002-0479-558X","last_name":"Fischer","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L"},{"full_name":"Laux, Tim","last_name":"Laux","first_name":"Tim"},{"full_name":"Simon, Theresa M.","last_name":"Simon","first_name":"Theresa M."}],"isi":1,"department":[{"_id":"JuFi"}],"doi":"10.1137/20M1322182","file":[{"file_size":310655,"file_name":"2020_SIAM_Fischer.pdf","success":1,"file_id":"9041","relation":"main_file","creator":"dernst","date_updated":"2021-01-25T07:48:39Z","checksum":"21aa1cf4c30a86a00cae15a984819b5d","access_level":"open_access","date_created":"2021-01-25T07:48:39Z","content_type":"application/pdf"}],"publication_status":"published","file_date_updated":"2021-01-25T07:48:39Z","has_accepted_license":"1","year":"2020","quality_controlled":"1","language":[{"iso":"eng"}],"scopus_import":"1","day":"15","publisher":"Society for Industrial and Applied Mathematics","page":"6222-6233","intvolume":"        52","acknowledgement":"This work was supported by the European Union's Horizon 2020 Research and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385 and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy, EXC-2047/1--390685813.","article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"_id":"9039","status":"public","oa_version":"Published Version","date_published":"2020-12-15T00:00:00Z","issue":"6","type":"journal_article","volume":52,"project":[{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385"}],"article_processing_charge":"No","citation":{"short":"J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis 52 (2020) 6222–6233.","apa":"Fischer, J. L., Laux, T., &#38; Simon, T. M. (2020). Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/20M1322182\">https://doi.org/10.1137/20M1322182</a>","chicago":"Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2020. <a href=\"https://doi.org/10.1137/20M1322182\">https://doi.org/10.1137/20M1322182</a>.","ama":"Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(6):6222-6233. doi:<a href=\"https://doi.org/10.1137/20M1322182\">10.1137/20M1322182</a>","ieee":"J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 6. Society for Industrial and Applied Mathematics, pp. 6222–6233, 2020.","mla":"Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 6, Society for Industrial and Applied Mathematics, 2020, pp. 6222–33, doi:<a href=\"https://doi.org/10.1137/20M1322182\">10.1137/20M1322182</a>.","ista":"Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis. 52(6), 6222–6233."}}