{"page":"297-383","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"JuFi"}],"language":[{"iso":"eng"}],"author":[{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser","first_name":"Maximilian","full_name":"Moser, Maximilian"}],"year":"2023","date_published":"2023-02-02T00:00:00Z","article_processing_charge":"No","publication":"Asymptotic Analysis","date_created":"2024-01-08T13:13:28Z","keyword":["General Mathematics"],"oa_version":"Preprint","type":"journal_article","citation":{"apa":"Moser, M. (2023). Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. <i>Asymptotic Analysis</i>. IOS Press. <a href=\"https://doi.org/10.3233/asy-221775\">https://doi.org/10.3233/asy-221775</a>","short":"M. Moser, Asymptotic Analysis 131 (2023) 297–383.","chicago":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” <i>Asymptotic Analysis</i>. IOS Press, 2023. <a href=\"https://doi.org/10.3233/asy-221775\">https://doi.org/10.3233/asy-221775</a>.","ieee":"M. Moser, “Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result,” <i>Asymptotic Analysis</i>, vol. 131, no. 3–4. IOS Press, pp. 297–383, 2023.","mla":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” <i>Asymptotic Analysis</i>, vol. 131, no. 3–4, IOS Press, 2023, pp. 297–383, doi:<a href=\"https://doi.org/10.3233/asy-221775\">10.3233/asy-221775</a>.","ista":"Moser M. 2023. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 131(3–4), 297–383.","ama":"Moser M. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. <i>Asymptotic Analysis</i>. 2023;131(3-4):297-383. doi:<a href=\"https://doi.org/10.3233/asy-221775\">10.3233/asy-221775</a>"},"doi":"10.3233/asy-221775","publication_identifier":{"issn":["0921-7134"],"eissn":["1875-8576"]},"_id":"14755","issue":"3-4","month":"02","title":"Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result","publication_status":"published","scopus_import":"1","oa":1,"publisher":"IOS Press","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.07100","open_access":"1"}],"acknowledgement":"The author gratefully acknowledges support through DFG, GRK 1692 “Curvature,\r\nCycles and Cohomology” during parts of the work.","day":"02","quality_controlled":"1","date_updated":"2024-01-09T09:22:16Z","intvolume":"       131","abstract":[{"text":"We consider the sharp interface limit for the scalar-valued and vector-valued Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse interface has developed and intersects the boundary ∂ Ω. The limit problem is mean curvature flow with 90°-contact angle and we show convergence in strong norms for well-prepared initial data as long as a smooth solution to the limit problem exists. To this end we assume that the limit problem has a smooth solution on [ 0 , T ] for some time T &gt; 0. Based on the latter we construct suitable curvilinear coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued Allen–Cahn equation. In order to estimate the difference of the exact and approximate solutions with a Gronwall-type argument, a spectral estimate for the linearized Allen–Cahn operator in both cases is required. The latter will be shown in a separate paper, cf. (Moser (2021)).","lang":"eng"}],"status":"public","article_type":"original","external_id":{"arxiv":["2105.07100"]},"volume":131}