{"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."}],"oa":1,"publication_identifier":{"eissn":["10957154"],"issn":["00361410"]},"publisher":"Society for Industrial and Applied Mathematics","intvolume":"        52","author":[{"orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","last_name":"Fischer","first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Tim","full_name":"Laux, Tim","last_name":"Laux"},{"first_name":"Theresa M.","full_name":"Simon, Theresa M.","last_name":"Simon"}],"external_id":{"isi":["000600695200027"]},"article_processing_charge":"No","department":[{"_id":"JuFi"}],"title":"Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies","doi":"10.1137/20M1322182","article_type":"original","project":[{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Published Version","scopus_import":"1","issue":"6","status":"public","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.","ddc":["510"],"year":"2020","type":"journal_article","publication":"SIAM Journal on Mathematical Analysis","date_published":"2020-12-15T00:00:00Z","citation":{"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>","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.","short":"J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis 52 (2020) 6222–6233.","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>.","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.","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>.","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>"},"volume":52,"_id":"9039","page":"6222-6233","month":"12","day":"15","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2021-01-25T07:48:39Z","tmp":{"short":"CC BY (4.0)","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)"},"file":[{"access_level":"open_access","file_id":"9041","relation":"main_file","date_created":"2021-01-25T07:48:39Z","checksum":"21aa1cf4c30a86a00cae15a984819b5d","success":1,"date_updated":"2021-01-25T07:48:39Z","file_name":"2020_SIAM_Fischer.pdf","content_type":"application/pdf","creator":"dernst","file_size":310655}],"ec_funded":1,"language":[{"iso":"eng"}],"isi":1,"date_updated":"2023-08-24T11:15:16Z","publication_status":"published","has_accepted_license":"1"}