{"id":"https://openalex.org/W7214586334","doi":"https://doi.org/10.48550/arxiv.2609.30412","title":"A phase-field model for the Verigin problem: weak solutions and sharp-interface limit","display_name":"A phase-field model for the Verigin problem: weak solutions and sharp-interface limit","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214586334","doi":"https://doi.org/10.48550/arxiv.2609.30412"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30412","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30412","pdf_url":"https://arxiv.org/pdf/2609.30412","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.30412","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037217364","display_name":"Anna Kubin","orcid":"https://orcid.org/0000-0003-0619-6211","observed_orcids":["https://orcid.org/0000-0003-0619-6211"]},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Kubin, Anna","raw_affiliation_strings":["Institut f\u00fcr Analysis und Scientific Computing , Technische Universit\u00e4t Wien , Wied- ner Hauptstrasse 8-10 , 1040 Vienna , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing , Technische Universit\u00e4t Wien , Wied- ner Hauptstrasse 8-10 , 1040 Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006089681","display_name":"Alice Marveggio","orcid":"https://orcid.org/0000-0001-5300-9867","observed_orcids":["https://orcid.org/0000-0001-5300-9867"]},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT","DE"],"is_corresponding":false,"raw_author_name":"Marveggio, Alice","raw_affiliation_strings":["Institut f\u00fcr Analysis und Scientific Computing , Technische Universit\u00e4t Wien , Wied- ner Hauptstrasse 8-10 , 1040 Vienna , Austria","Institute for Applied Mathematics , Universit\u00e4t Bonn , Endenicher Allee 62 , 53115 Bonn , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing , Technische Universit\u00e4t Wien , Wied- ner Hauptstrasse 8-10 , 1040 Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Applied Mathematics , Universit\u00e4t Bonn , Endenicher Allee 62 , 53115 Bonn , Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.4968000054359436,"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"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.4968000054359436,"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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.3402999937534332,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.04749999940395355,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-field-model","display_name":"phase-field model","score":0.9340000152587891},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.7680000066757202},{"id":"https://openalex.org/keywords/weak-solutions","display_name":"weak solutions","score":0.9449999928474426},{"id":"https://openalex.org/keywords/sharp-interface-limit","display_name":"sharp interface limit","score":0.9980000257492065},{"id":"https://openalex.org/keywords/strong-compactness","display_name":"strong compactness","score":0.7599999904632568},{"id":"https://openalex.org/keywords/perimeter","display_name":"perimeter","score":0.8930000066757202}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8410000205039978},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7190999984741211},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.6809999942779541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6786999702453613},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6349999904632568},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.6301000118255615},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.5823000073432922},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.5084999799728394},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4650999903678894},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.46239998936653137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44670000672340393},{"id":"https://openalex.org/C153919410","wikidata":"https://www.wikidata.org/wiki/Q9993851","display_name":"Weak formulation","level":3,"score":0.3993000090122223},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32589998841285706},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C2983502797","wikidata":"https://www.wikidata.org/wiki/Q828402","display_name":"Energy density","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28110000491142273},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27090001106262207},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2669999897480011}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30412","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30412","pdf_url":"https://arxiv.org/pdf/2609.30412","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2609.30412","doi":"https://doi.org/10.48550/arxiv.2609.30412","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30412","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.30412","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30412","pdf_url":"https://arxiv.org/pdf/2609.30412","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5686947098","display_name":null,"funder_award_id":"539309657","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6080645987","display_name":"Tunable Materials: Geometry, Nonlocality, Chirality","funder_award_id":"Y 1292","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7416782364","display_name":"Alternate minimization in fracture mechanics","funder_award_id":"P 35359","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8265043617","display_name":null,"funder_award_id":"CRC 1720","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G9000043132","display_name":null,"funder_award_id":"10.55776/P35359","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G9000057332","display_name":null,"funder_award_id":"10.55776/Y1292","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214586334.pdf","grobid_xml":"https://content.openalex.org/works/W7214586334.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7126100311","https://openalex.org/W7204580263"],"related_works":["https://openalex.org/W7126100311","https://openalex.org/W1980161380","https://openalex.org/W2133797025","https://openalex.org/W2802934244","https://openalex.org/W7213343163","https://openalex.org/W1481086287","https://openalex.org/W4200283732","https://openalex.org/W1977069588","https://openalex.org/W2043380834","https://openalex.org/W3112917280"],"abstract_inverted_index":{"We":[0,50],"introduce":[1],"a":[2,23,28,91],"novel":[3],"phase-field":[4],"model":[5],"approximating":[6],"the":[7,32,39,53,67,77,83,95],"Verigin":[8,96],"problem":[9,97],"with":[10,34,98],"phase":[11,40,70,99],"transition.":[12],"For":[13,58],"fixed":[14],"interface":[15],"thickness":[16],"$\\varepsilon>0$,":[17],"we":[18,62,73],"construct":[19],"weak":[20,92],"solutions":[21],"through":[22],"time-discrete":[24],"variational":[25],"scheme":[26],"combining":[27],"Wasserstein":[29],"minimizing-movement":[30],"for":[31,38],"density":[33],"Sch\u00e4tzle's":[35],"selection":[36],"procedure":[37],"field,":[41],"which":[42],"yields":[43],"strong":[44,64],"compactness":[45,65],"and":[46,69,72],"an":[47,102],"almost-minimizing":[48],"property.":[49],"then":[51],"investigate":[52],"sharp-interface":[54],"limit":[55],"$\\varepsilon":[56],"\\downarrow0$.":[57],"well-prepared":[59],"initial":[60],"data,":[61],"establish":[63],"of":[66,76,94],"densities":[68],"fields,":[71],"prove":[74],"convergence":[75],"time-integrated":[78],"diffuse":[79],"interfacial":[80],"energy":[81,104],"to":[82],"perimeter.":[84],"The":[85],"limiting":[86],"evolution":[87],"is":[88],"identified":[89],"as":[90],"solution":[93],"transition,":[100],"satisfying":[101],"optimal":[103],"dissipation":[105],"inequality.":[106]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-29T00:00:00"}