{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:53Z","timestamp":1787318813179,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 1692"],"award-info":[{"award-number":["GRK 1692"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolving family of curves driven by curve diffusion flow, which has free boundary points supported on a line. The evolving curve has a fixed contact angle $\\alpha \\in (0, \\pi)$ with that line and satisfies a no-flux condition. The proof is led by contradiction: A compactness argument combined with the short time existence result enables us to extend the flow, which contradicts the maximality of the solution.<\/jats:p>","DOI":"10.1137\/19m1242914","type":"journal-article","created":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T10:37:35Z","timestamp":1591007855000},"page":"2592-2623","source":"Crossref","is-referenced-by-count":3,"title":["A Blow-up Criterion for the Curve Diffusion Flow with a Contact Angle"],"prefix":"10.1137","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6606-4352","authenticated-orcid":true,"given":"Helmut","family":"Abels","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julia","family":"Butz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,6,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2019.08.018"},{"key":"atypb2","volume-title":"Universitext","author":"Alt H. 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Butz,\n                      The Curve Diffusion Flow with a Contact Angle\n                      , PhD thesis, 2018, Universit\u00e4t Regonsburg; also available online from https:\/\/epub.uni-regensburg.de\/37705\/."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792500002369"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.14492\/hokmj\/1350652421"},{"key":"atypb8","first-page":"209","volume":"34","author":"Dall'Acqua A.","year":"2014","journal-title":"Analysis (Berlin)"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.4310\/CAG.2014.v22.n4.a2"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2016.04.027"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141001383709"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141097320675"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.57262\/ade\/1356651336"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2012.03.010"},{"key":"atypb15","volume-title":"Mod. Birkh\u00e4user Class.","author":"Lunardi A.","year":"1995"},{"key":"atypb16","unstructured":"M. Meyries,\n                      Maximal Regularity in Weighted Spaces, Nonlinear Boundary Conditions, and Global Attractors\n                      , PhD thesis, 2010,https:\/\/publikationen.bibliothek.kit.edu\/1000021198."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2011.11.001"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1002\/mana.201100057"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1063\/1.1722742"},{"key":"atypb20","first-page":"27698","volume-title":"Birkh\u00e4user","author":"Pr\u00fcss J.","year":"2016"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/BF01765315"},{"key":"atypb22","volume-title":"Function Spaces, Differential Operators","author":"Triebel H.","year":"1995","edition":"2"},{"key":"atypb23","volume-title":"Curve Diffusion and Straightening Flows on Parallel Lines, preprint, https:\/\/arxiv.org\/abs\/1703.10711","author":"Wheeler G.","year":"2017"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4838-5"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1242914","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:41:13Z","timestamp":1787316073000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1242914"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1242914"],"URL":"https:\/\/doi.org\/10.1137\/19m1242914","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}