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Simon, “Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,” SIAM Journal on Mathematical Analysis, vol. 52, no. 6. Society for Industrial and Applied Mathematics, pp. 6222–6233, 2020.","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.","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.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2020. https://doi.org/10.1137/20M1322182.","apa":"Fischer, J. L., Laux, T., & Simon, T. M. (2020). Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1322182","short":"J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis 52 (2020) 6222–6233."},"uri_base":"https://research-explorer.ista.ac.at","has_accepted_license":"1","dc":{"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1137/20M1322182","info:eu-repo/semantics/altIdentifier/issn/00361410","info:eu-repo/semantics/altIdentifier/issn/10957154","info:eu-repo/semantics/altIdentifier/wos/000600695200027","info:eu-repo/grantAgreement/EC/H2020/665385"],"rights":["info:eu-repo/semantics/openAccess"],"creator":["Fischer, Julian L","Laux, Tim","Simon, Theresa M."],"title":["Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies"],"identifier":["https://research-explorer.ista.ac.at/record/9039","https://research-explorer.ista.ac.at/download/9039/9041"],"date":["2020"],"publisher":["Society for Industrial and Applied Mathematics"],"source":["Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis. 2020;52(6):6222-6233. doi:10.1137/20M1322182"],"subject":["ddc:510"],"description":["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."],"language":["eng"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"]},"article_type":"original","language":[{}],"day":"15","status":"public","department":[{"_id":"JuFi","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"volume":52,"author":[{"orcid":"0000-0002-0479-558X","first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer"},{"first_name":"Tim","last_name":"Laux"},{"last_name":"Simon","first_name":"Theresa M."}],"dini_type":"doc-type:article","publication_identifier":{"eissn":[],"issn":[]},"abstract":[{"lang":"eng"}],"ddc":[],"ec_funded":1,"oa":1,"project":[{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"issue":"6","date_created":"2021-01-24T23:01:09Z","external_id":{"isi":[]},"date_updated":"2023-08-24T11:15:16Z","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.","creator":{"id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","login":"dernst"},"quality_controlled":"1","_id":"9039","file":[{"date_created":"2021-01-25T07:48:39Z","checksum":"21aa1cf4c30a86a00cae15a984819b5d","file_size":310655,"date_updated":"2021-01-25T07:48:39Z","relation":"main_file","creator":"dernst","file_id":"9041","file_name":"2020_SIAM_Fischer.pdf","success":1,"access_level":"open_access","content_type":"application/pdf"}],"isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"}]