{"id":"https://openalex.org/W4406084207","doi":"https://doi.org/10.1137/24m1644523","title":"A Rigorous Approach to the Sharp Interface Limit for Phase-Field Models of Tumor Growth","display_name":"A Rigorous Approach to the Sharp Interface Limit for Phase-Field Models of Tumor Growth","publication_year":2025,"publication_date":"2025-01-06","ids":{"openalex":"https://openalex.org/W4406084207","doi":"https://doi.org/10.1137/24m1644523"},"language":"en","primary_location":{"id":"doi:10.1137/24m1644523","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1644523","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/A5048124364","display_name":"Filippo Riva","orcid":"https://orcid.org/0000-0002-7855-1262"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Filippo Riva","raw_affiliation_strings":["Dipartimento di Matematica \u201cFelice Casorati\u201d, Universit\u00e0 degli Studi di Pavia, 27100 Pavia, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7855-1262","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cFelice Casorati\u201d, Universit\u00e0 degli Studi di Pavia, 27100 Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017446516","display_name":"Elisabetta Rocca","orcid":"https://orcid.org/0000-0002-9930-907X"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Elisabetta Rocca","raw_affiliation_strings":["Dipartimento di Matematica \u201cFelice Casorati\u201d, Universit\u00e0 degli Studi di Pavia, IMATI-C.N.R., 27100, Pavia, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9930-907X","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cFelice Casorati\u201d, Universit\u00e0 degli Studi di Pavia, IMATI-C.N.R., 27100, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I25217355"],"apc_list":null,"apc_paid":null,"fwci":0.7136,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59618557,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":94},"biblio":{"volume":"57","issue":"1","first_page":"65","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9976999759674072,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.988099992275238,"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/mathematics","display_name":"Mathematics","score":0.8087500929832458},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.679951012134552},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5404421091079712},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5360432267189026},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5276119709014893},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.45715659856796265},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3452083170413971},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3282780945301056},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15599727630615234},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.11483842134475708},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1062464714050293}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8087500929832458},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.679951012134552},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5404421091079712},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5360432267189026},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5276119709014893},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.45715659856796265},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3452083170413971},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3282780945301056},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15599727630615234},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.11483842134475708},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1062464714050293},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1644523","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1644523","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6296201990","display_name":null,"funder_award_id":"P2022Z7ZAJ","funder_id":"https://openalex.org/F7311471023","funder_display_name":"NextGenerationEU"}],"funders":[{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":"https://ror.org/02ktjph70"},{"id":"https://openalex.org/F7311471023","display_name":"NextGenerationEU","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W11579564","https://openalex.org/W114949804","https://openalex.org/W195141885","https://openalex.org/W1512153219","https://openalex.org/W1593414945","https://openalex.org/W1605821011","https://openalex.org/W2029982392","https://openalex.org/W2045434770","https://openalex.org/W2088130948","https://openalex.org/W2095917371","https://openalex.org/W2104010300","https://openalex.org/W2111564493","https://openalex.org/W2112144602","https://openalex.org/W2138618054","https://openalex.org/W2148146770","https://openalex.org/W2162515576","https://openalex.org/W2171422900","https://openalex.org/W2424838513","https://openalex.org/W2594425100","https://openalex.org/W2606617955","https://openalex.org/W2913832872","https://openalex.org/W2962777676","https://openalex.org/W2962823729","https://openalex.org/W2962965237","https://openalex.org/W2963161190","https://openalex.org/W2963181663","https://openalex.org/W2963244207","https://openalex.org/W2963298160","https://openalex.org/W2963683463","https://openalex.org/W2963768558","https://openalex.org/W2964078192","https://openalex.org/W3088400485","https://openalex.org/W3105707937","https://openalex.org/W3112433806","https://openalex.org/W3198397443","https://openalex.org/W3215884613","https://openalex.org/W4234794606","https://openalex.org/W4308117222","https://openalex.org/W4386710551","https://openalex.org/W4391133233","https://openalex.org/W4392523184"],"related_works":["https://openalex.org/W2353396818","https://openalex.org/W2378005410","https://openalex.org/W2370473919","https://openalex.org/W1973641256","https://openalex.org/W2170435352","https://openalex.org/W2762984199","https://openalex.org/W2048876619","https://openalex.org/W2390496461","https://openalex.org/W2389654532","https://openalex.org/W2384763348"],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2],"paper":[3],"we":[4,47],"consider":[5],"two":[6,39],"diffuse":[7,56,63],"interface":[8,57,64,68],"models":[9,32,65],"for":[10,18,28,111,120],"tumor":[11,20,113],"growth":[12],"coupling":[13,41],"a":[14,24],"Cahn\u2013Hilliard":[15],"type":[16,26,109],"equation":[17,27,119],"the":[19,29,36,49,52,55,112,118,121],"phase":[21],"parameter":[22,58],"to":[23,60,66,103,107],"reaction-diffusion":[25],"nutrient.":[30,122],"The":[31,98],"are":[33],"distinguished":[34],"by":[35],"presence":[37],"of":[38,51],"different":[40],"source":[42],"terms.":[43],"For":[44],"such":[45],"problems,":[46],"address":[48],"question":[50],"limit,":[53],"as":[54],"tends":[59],"zero,":[61],"from":[62],"sharp":[67],"ones,":[69],"justifying":[70],"rigorously":[71],"what":[72],"was":[73],"deduced":[74],"via":[75],"formal":[76],"asymptotics":[77],"in":[78],"[H.":[79],"Garcke,":[80],"K.":[81],"F.":[82],"Lam,":[83],"E.":[84],"Sitka,":[85],"and":[86],"V.":[87],"Styles,":[88],"Math.":[89],"Models":[90],"Methods":[91],"Appl.":[92],"Sci.,":[93],"26":[94],"(2016),":[95],"pp.":[96],"1095\u20131148].":[97],"resulting":[99],"evolutions":[100],"turn":[101],"out":[102],"be":[104],"varifold":[105],"solutions":[106],"Mullins\u2013Sekerka":[108],"flows":[110],"region":[114],"suitably":[115],"coupled":[116],"with":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}