{"id":"https://openalex.org/W4392089949","doi":"https://doi.org/10.1137/24m1715325","title":"Higher-Order Singular Perturbation Models for Phase Transitions","display_name":"Higher-Order Singular Perturbation Models for Phase Transitions","publication_year":2025,"publication_date":"2025-06-11","ids":{"openalex":"https://openalex.org/W4392089949","doi":"https://doi.org/10.1137/24m1715325"},"language":"en","primary_location":{"id":"doi:10.1137/24m1715325","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1715325","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2402.13626","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013246581","display_name":"Giuseppe Cosma Brusca","orcid":null},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppe Cosma Brusca","raw_affiliation_strings":["SISSA, via Bonomea, 265 34146, Trieste, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SISSA, via Bonomea, 265 34146, Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056929234","display_name":"Davide Donati","orcid":"https://orcid.org/0000-0003-2952-8813"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Davide Donati","raw_affiliation_strings":["SISSA, via Bonomea, 265 34146, Trieste, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SISSA, via Bonomea, 265 34146, Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032298754","display_name":"Margherita Solci","orcid":"https://orcid.org/0000-0001-5800-7924"},"institutions":[{"id":"https://openalex.org/I159650629","display_name":"University of Sassari","ror":"https://ror.org/01bnjbv91","country_code":"IT","type":"education","lineage":["https://openalex.org/I159650629"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Margherita Solci","raw_affiliation_strings":["DADU, Universit\u00e0 di Sassari, piazza Duomo 6, 07041 Alghero, Italy"],"raw_orcid":"https://orcid.org/0000-0001-5800-7924","affiliations":[{"raw_affiliation_string":"DADU, Universit\u00e0 di Sassari, piazza Duomo 6, 07041 Alghero, Italy","institution_ids":["https://openalex.org/I159650629"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7749,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65356779,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"57","issue":"3","first_page":"3146","last_page":"3170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.5468000173568726,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.5468000173568726,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.5386999845504761,"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/perturbation","display_name":"Perturbation (astronomy)","score":0.5958465337753296},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5946305990219116},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.525711715221405},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.47476887702941895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44412729144096375},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35497575998306274},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3376418948173523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27523642778396606},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.1602655053138733},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15339985489845276},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11706700921058655}],"concepts":[{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5958465337753296},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5946305990219116},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.525711715221405},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.47476887702941895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44412729144096375},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35497575998306274},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3376418948173523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27523642778396606},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.1602655053138733},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15339985489845276},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11706700921058655},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/24m1715325","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1715325","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:2402.13626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.13626","pdf_url":"https://arxiv.org/pdf/2402.13626","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2402.13626","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2402.13626","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2402.13626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.13626","pdf_url":"https://arxiv.org/pdf/2402.13626","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4392089949.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W2091503868","https://openalex.org/W2598510391","https://openalex.org/W1990890346","https://openalex.org/W2899703448","https://openalex.org/W2079935585","https://openalex.org/W4293874319","https://openalex.org/W1981490278","https://openalex.org/W2068826680","https://openalex.org/W2042833347","https://openalex.org/W4382024802","https://openalex.org/W2025092517","https://openalex.org/W2003878476","https://openalex.org/W2048437024","https://openalex.org/W4307444511","https://openalex.org/W1514949711","https://openalex.org/W2018661409","https://openalex.org/W2905752022","https://openalex.org/W585462275","https://openalex.org/W4229690478","https://openalex.org/W1990541396","https://openalex.org/W2001726251","https://openalex.org/W2963550031"],"related_works":["https://openalex.org/W2011339542","https://openalex.org/W2055379029","https://openalex.org/W2387203662","https://openalex.org/W2332818190","https://openalex.org/W4388569548","https://openalex.org/W4327639758","https://openalex.org/W2116787190","https://openalex.org/W2154304710","https://openalex.org/W2019676381","https://openalex.org/W2006371715"],"abstract_inverted_index":{"Variational":[0],"models":[1],"of":[2,25,45,51,97,144,148,164],"phase":[3],"transitions":[4],"take":[5],"into":[6],"account":[7],"double-well":[8,47],"energies":[9],"singularly":[10],"perturbed":[11],"by":[12,23,36,49,87,115],"gradient":[13],"terms,":[14],"such":[15,30],"as":[16,63],"the":[17,61,65,77,82,95,102,106,125,128,156],"Cahn-Hilliard":[18],"free":[19],"energy.":[20],"The":[21,91],"derivation":[22,96],"$\u0393$-convergence":[24],"a":[26,33,42,46,69,137],"sharp-interface":[27],"limit":[28,62],"for":[29],"energy":[31,48,72,108,152,168],"is":[32,94],"classical":[34],"result":[35],"Modica":[37],"and":[38,54,80,89,158,167],"Mortola.":[39],"We":[40],"consider":[41],"singular":[43],"perturbation":[44],"derivatives":[50,126],"order":[52,132],"$k$,":[53],"show":[55],"that":[56,135],"we":[57],"still":[58],"can":[59],"describe":[60],"in":[64,74,162],"case":[66,78,83],"$k=1$":[67,79],"with":[68,76,81,121,150],"suitable":[70],"interfacial":[71,107],"density,":[73,109],"accord":[75],"$k=2$":[84],"previously":[85],"analyzed":[86],"Fonseca":[88],"Mantegazza.":[90],"main":[92],"isssue":[93],"an":[98],"optimal-profile":[99],"problem":[100],"on":[101,118,124,143],"real":[103],"line":[104],"describing":[105],"which":[110],"must":[111,140],"be":[112,141],"conveniently":[113],"approximated":[114],"minimum":[116],"problems":[117],"finite":[119],"intervals":[120],"homogeneous":[122],"condition":[123],"at":[127],"endpoints":[129],"up":[130],"to":[131,155],"$k-1$.":[133],"To":[134],"end":[136],"careful":[138],"study":[139],"carried":[142],"sets":[145],"where":[146],"sequences":[147],"functions":[149],"equibounded":[151],"are":[153],"``close":[154],"wells''":[157],"have":[159],"``small":[160],"derivatives'',":[161],"terms":[163],"interpolation":[165],"inequalities":[166],"estimates.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2024-02-23T00:00:00"}
