{"id":"https://openalex.org/W2025790272","doi":"https://doi.org/10.1137/04060528x","title":"Regularization by Kinetic Undercooling of Blow-up in the Ill-posed Stefan Problem","display_name":"Regularization by Kinetic Undercooling of Blow-up in the Ill-posed Stefan Problem","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2025790272","doi":"https://doi.org/10.1137/04060528x","mag":"2025790272"},"language":"en","primary_location":{"id":"doi:10.1137/04060528x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/04060528x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5010038899","display_name":"John R. King","orcid":"https://orcid.org/0000-0002-6228-8375"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. R. King","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024047853","display_name":"Jonathan D. Evans","orcid":"https://orcid.org/0000-0002-2565-0566"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. D. Evans","raw_affiliation_strings":["Department of Mathematical Sciences"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010038899"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3465,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.81368785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"5","first_page":"1677","last_page":"1707"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"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/T10670","display_name":"Aluminum Alloy Microstructure Properties","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/supercooling","display_name":"Supercooling","score":0.850361704826355},{"id":"https://openalex.org/keywords/dimensionless-quantity","display_name":"Dimensionless quantity","score":0.7305502891540527},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.6520220041275024},{"id":"https://openalex.org/keywords/stefan-problem","display_name":"Stefan problem","score":0.6118669509887695},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5961071252822876},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5539238452911377},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5101502537727356},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.506466269493103},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.493147075176239},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4568234086036682},{"id":"https://openalex.org/keywords/latent-heat","display_name":"Latent heat","score":0.45157095789909363},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4173037111759186},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38907402753829956},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.3876926004886627},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3111688494682312},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20155572891235352},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.12318503856658936},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.09042668342590332},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07043874263763428},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06593886017799377}],"concepts":[{"id":"https://openalex.org/C112964491","wikidata":"https://www.wikidata.org/wiki/Q213659","display_name":"Supercooling","level":2,"score":0.850361704826355},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.7305502891540527},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.6520220041275024},{"id":"https://openalex.org/C2778021227","wikidata":"https://www.wikidata.org/wiki/Q3775789","display_name":"Stefan problem","level":3,"score":0.6118669509887695},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5961071252822876},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5539238452911377},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5101502537727356},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.506466269493103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.493147075176239},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4568234086036682},{"id":"https://openalex.org/C58024561","wikidata":"https://www.wikidata.org/wiki/Q207721","display_name":"Latent heat","level":2,"score":0.45157095789909363},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4173037111759186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38907402753829956},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3876926004886627},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3111688494682312},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20155572891235352},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.12318503856658936},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.09042668342590332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07043874263763428},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06593886017799377},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/04060528x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/04060528x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W182318076","https://openalex.org/W763664720","https://openalex.org/W1492913691","https://openalex.org/W1965523819","https://openalex.org/W1975721862","https://openalex.org/W1976258210","https://openalex.org/W1987209350","https://openalex.org/W1990533693","https://openalex.org/W2004339123","https://openalex.org/W2011040928","https://openalex.org/W2012697931","https://openalex.org/W2018459441","https://openalex.org/W2020797226","https://openalex.org/W2022634717","https://openalex.org/W2024919497","https://openalex.org/W2025730140","https://openalex.org/W2025739397","https://openalex.org/W2030697990","https://openalex.org/W2036153540","https://openalex.org/W2040336935","https://openalex.org/W2049235379","https://openalex.org/W2051243927","https://openalex.org/W2055981352","https://openalex.org/W2062310403","https://openalex.org/W2062813971","https://openalex.org/W2067001772","https://openalex.org/W2071305297","https://openalex.org/W2078483116","https://openalex.org/W2079021686","https://openalex.org/W2086329729","https://openalex.org/W2095410276","https://openalex.org/W2115329200","https://openalex.org/W2121711024","https://openalex.org/W2131223202","https://openalex.org/W2525357764","https://openalex.org/W2561126521","https://openalex.org/W2563898196","https://openalex.org/W2696713045","https://openalex.org/W4205594596","https://openalex.org/W4213137427"],"related_works":["https://openalex.org/W2010932039","https://openalex.org/W4311259703","https://openalex.org/W2093581706","https://openalex.org/W2484533320","https://openalex.org/W2463965720","https://openalex.org/W2047584694","https://openalex.org/W1971052587","https://openalex.org/W4293775294","https://openalex.org/W1970500014","https://openalex.org/W2307724024"],"abstract_inverted_index":{"It":[0,85],"is":[1,86,118,124,143],"well":[2],"known":[3],"that":[4,12],"the":[5,41,52,59,62,65,81,92,100,105,113,125,130,134,144],"one-dimensional":[6],"supercooled":[7],"Stefan":[8],"problem":[9],"possesses":[10],"solutions":[11,22,72],"blow":[13],"up":[14],"in":[15,89,109,136],"finite":[16,126],"time.":[17],"The":[18,69],"asymptotics":[19,70],"of":[20,43,54,61,71,80],"such":[21,55],"have":[23],"been":[24],"analyzed":[25],"by":[26,99,104,120],"Herrero":[27],"and":[28,57,73,103],"Velazquez":[29],"[European":[30],"J.":[31],"Appl.":[32],"Math.,":[33],"7":[34],"(1996),":[35],"pp.":[36],"119--150].":[37],"Here":[38],"we":[39],"consider":[40],"effect":[42],"kinetic":[44,82],"undercooling":[45,83],"as":[46],"a":[47],"regularizing":[48],"mechanism":[49],"to":[50],"prevent":[51],"formation":[53],"singularities":[56],"study":[58],"continuation":[60],"solution":[63],"through":[64],"\"near":[66],"blow-up\"":[67],"regime.":[68],"interfaces":[74],"are":[75],"described":[76],"for":[77],"small":[78],"values":[79],"parameter.":[84],"shown":[87],"that,":[88],"this":[90],"limit,":[91],"interface":[93,131],"jumps":[94,132],"over":[95,133],"an":[96],"interval":[97,135],"determined":[98],"latent":[101,145],"heat":[102],"initial":[106],"data.":[107],"Specifically,":[108],"dimensionless":[110],"variables,":[111],"if":[112],"temperature":[114],"profile":[115],"at":[116],"blow-up":[117,127],"denoted":[119],"u(x,t_c^-)$,":[121],"where":[122,141],"$t_c$":[123],"time,":[128],"then":[129],"which":[137],"$u(x,t_c^-)":[138],"<":[139],"-\\lambda$,":[140],"$\\lambda$":[142],"heat.":[146]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}