{"id":"https://openalex.org/W2032139369","doi":"https://doi.org/10.1137/060660369","title":"A Class of Free Boundary Problems with Onset of a New Phase","display_name":"A Class of Free Boundary Problems with Onset of a New Phase","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2032139369","doi":"https://doi.org/10.1137/060660369","mag":"2032139369"},"language":"en","primary_location":{"id":"doi:10.1137/060660369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660369","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0610771","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Patrick Guidotti","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Patrick Guidotti","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9106,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71143305,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"6","first_page":"1981","last_page":"2004"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.4244999885559082,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.4244999885559082,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.07800000160932541,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.07599999755620956,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6186000108718872},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5900999903678894},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5848000049591064},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.5471000075340271},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.546500027179718},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.46389999985694885},{"id":"https://openalex.org/keywords/singular-solution","display_name":"Singular solution","score":0.462799996137619}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8783000111579895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6699000000953674},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6186000108718872},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5900999903678894},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5848000049591064},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.5471000075340271},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.546500027179718},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.46389999985694885},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.462799996137619},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.41449999809265137},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3817000091075897},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.34790000319480896},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.3418999910354614},{"id":"https://openalex.org/C106947605","wikidata":"https://www.wikidata.org/wiki/Q3278575","display_name":"Cauchy boundary condition","level":4,"score":0.3386000096797943},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.31299999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060660369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660369","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:arXiv.org:math/0610771","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0610771","pdf_url":"https://arxiv.org/pdf/math/0610771","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0610771","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0610771","pdf_url":"https://arxiv.org/pdf/math/0610771","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1536136046","https://openalex.org/W1968268700","https://openalex.org/W1988297408","https://openalex.org/W1998378225","https://openalex.org/W2007028807","https://openalex.org/W2013688493","https://openalex.org/W2025730140","https://openalex.org/W2038027713","https://openalex.org/W2041467324","https://openalex.org/W2051243927","https://openalex.org/W2065729228","https://openalex.org/W2088883807","https://openalex.org/W4205594596","https://openalex.org/W4213137427"],"related_works":[],"abstract_inverted_index":{"A":[0],"class":[1],"of":[2,16,28,37,114],"diffusion\u2010driven":[3],"free":[4,30,107],"boundary":[5,50,108],"problems":[6,96,109,123],"is":[7,10,97],"considered":[8],"which":[9],"characterized":[11],"by":[12,20],"the":[13,26,29,59,101,106,119],"initial":[14,49],"onset":[15],"a":[17,33,46,54,86],"phase":[18],"and":[19,53,71],"an":[21,126],"explicit":[22],"kinematic":[23],"condition":[24],"for":[25,79,91,105,118],"evolution":[27],"boundary.":[31],"By":[32],"domain":[34],"fixing":[35],"change":[36],"variables":[38],"it":[39],"naturally":[40],"leads":[41],"to":[42,99],"coupled":[43],"systems":[44],"comprising":[45],"singular":[47,93,122],"parabolic":[48,94],"value":[51],"problem":[52],"Hamilton\u2013Jacobi":[55],"equation.":[56],"Even":[57],"though":[58],"one\u2010dimensional":[60],"case":[61],"has":[62],"been":[63,77],"thoroughly":[64],"investigated,":[65],"results":[66,104,117],"as":[67,69],"basic":[68],"well\u2010posedness":[70,103],"regularity":[72,89,116],"have":[73],"so":[74],"far":[75],"not":[76],"obtained":[78],"its":[80],"higher\u2010dimensional":[81],"counterpart.":[82],"In":[83],"this":[84],"paper":[85],"recently":[87],"developed":[88],"theory":[90],"abstract":[92],"Cauchy":[95],"utilized":[98],"obtain":[100],"first":[102],"under":[110],"consideration.":[111],"The":[112],"derivation":[113],"elliptic":[115],"underlying":[120],"static":[121],"will":[124],"play":[125],"important":[127],"role.":[128]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
