{"id":"https://openalex.org/W1970474851","doi":"https://doi.org/10.1137/s0036141001383709","title":"Evolution of Elastic Curves in $\\Rn$: Existence and Computation","display_name":"Evolution of Elastic Curves in $\\Rn$: Existence and Computation","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1970474851","doi":"https://doi.org/10.1137/s0036141001383709","mag":"1970474851"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141001383709","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001383709","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089965962","display_name":"Gerhard Dziuk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gerhard Dziuk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077962251","display_name":"Ernst Kuwert","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ernst Kuwert","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052437262","display_name":"Reiner Sch\u00e4tzle","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reiner Schatzle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9511,"has_fulltext":false,"cited_by_count":213,"citation_normalized_percentile":{"value":0.95302816,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"33","issue":"5","first_page":"1228","last_page":"1245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8387840986251831},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.7215163707733154},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.7022001147270203},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6389362812042236},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.607736349105835},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5904199481010437},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.577705442905426},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5372085571289062},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.523363471031189},{"id":"https://openalex.org/keywords/elastic-energy","display_name":"Elastic energy","score":0.43304091691970825},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37035325169563293},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08412402868270874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0732755959033966}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8387840986251831},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7215163707733154},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7022001147270203},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6389362812042236},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.607736349105835},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5904199481010437},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.577705442905426},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5372085571289062},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.523363471031189},{"id":"https://openalex.org/C14041564","wikidata":"https://www.wikidata.org/wiki/Q891408","display_name":"Elastic energy","level":2,"score":0.43304091691970825},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37035325169563293},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08412402868270874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0732755959033966},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036141001383709","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001383709","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:freidok.uni-freiburg.de:46485","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/46485","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis. - 33, 5 (2002) , 1228-1245, ISSN: 0036-1410","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/12","display_name":"Responsible consumption and production","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1487335813","https://openalex.org/W1514872062","https://openalex.org/W1968082077","https://openalex.org/W1974645249","https://openalex.org/W1979743485","https://openalex.org/W1999296146","https://openalex.org/W2050059859","https://openalex.org/W2064152620","https://openalex.org/W2070338430","https://openalex.org/W2083391393","https://openalex.org/W2085945334"],"related_works":["https://openalex.org/W2376287735","https://openalex.org/W4297783372","https://openalex.org/W2786783041","https://openalex.org/W4288351025","https://openalex.org/W2945123146","https://openalex.org/W4318145980","https://openalex.org/W2901766321","https://openalex.org/W3087656105","https://openalex.org/W4287825832","https://openalex.org/W1970474851"],"abstract_inverted_index":{"We":[0,64],"consider":[1],"curves":[2],"in":[3,24,90],"${\\mathbb":[4],"R}^n$":[5],"moving":[6],"by":[7],"the":[8,15,25,36,39,53,58,69,73],"gradient":[9],"flow":[10,61],"for":[11,52,67],"elastic":[12,70],"energy,":[13],"i.e.,":[14],"L2":[16],"integral":[17],"of":[18,31,55,87],"curvature.":[19],"Long-time":[20],"existence":[21],"is":[22,33,41,62],"proved":[23],"two":[26],"cases":[27,86],"when":[28],"a":[29,44,49,78,92],"multiple":[30],"length":[32,40],"added":[34],"to":[35,57],"energy":[37],"or":[38],"fixed":[42],"as":[43],"constraint.":[45],"Along":[46],"these":[47],"lines,":[48],"lower":[50],"bound":[51],"lifespan":[54],"solutions":[56],"curve":[59,74,88],"diffusion":[60,75,89],"observed.":[63],"derive":[65],"algorithms":[66],"both":[68],"flows":[71],"and":[72],"equation.":[76],"After":[77],"numerical":[79],"test":[80],"we":[81],"compute":[82],"several":[83],"examples,":[84],"including":[85],"which":[91],"singularity":[93],"develops.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":20},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}