{"id":"https://openalex.org/W4387407031","doi":"https://doi.org/10.1137/22m1540429","title":"Convergence of Solutions to a Convective Cahn\u2013Hilliard-Type Equation of the Sixth Order in Case of Small Deposition Rates","display_name":"Convergence of Solutions to a Convective Cahn\u2013Hilliard-Type Equation of the Sixth Order in Case of Small Deposition Rates","publication_year":2023,"publication_date":"2023-10-06","ids":{"openalex":"https://openalex.org/W4387407031","doi":"https://doi.org/10.1137/22m1540429"},"language":"en","primary_location":{"id":"doi:10.1137/22m1540429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1540429","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":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019510066","display_name":"Piotr Rybka","orcid":"https://orcid.org/0000-0002-0694-8201"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Piotr Rybka","raw_affiliation_strings":["Institute of Applied Mathematics and Mechanics, the University of Warsaw, 02-097 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics and Mechanics, the University of Warsaw, 02-097 Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052058766","display_name":"Glen Wheeler","orcid":"https://orcid.org/0000-0003-3314-5647"},"institutions":[{"id":"https://openalex.org/I204824540","display_name":"University of Wollongong","ror":"https://ror.org/00jtmb277","country_code":"AU","type":"education","lineage":["https://openalex.org/I204824540"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Glen Wheeler","raw_affiliation_strings":["School of Mathematics and Applied Statistics, University of\u00a0Wollongong, Wollongong, 2522 NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Applied Statistics, University of\u00a0Wollongong, Wollongong, 2522 NSW, Australia","institution_ids":["https://openalex.org/I204824540"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019510066"],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09494093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"5","first_page":"5823","last_page":"5861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9980999827384949,"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":0.9980999827384949,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9952999949455261,"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/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8301922082901001},{"id":"https://openalex.org/keywords/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.6188321709632874},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5898157954216003},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.581206738948822},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.580867350101471},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.574353039264679},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5734308958053589},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.564591109752655},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.5512201189994812},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5268755555152893},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5164933204650879},{"id":"https://openalex.org/keywords/sense","display_name":"Sense (electronics)","score":0.41273078322410583},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.19987517595291138},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15568271279335022},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1193644106388092},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10260340571403503}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8301922082901001},{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.6188321709632874},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5898157954216003},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.581206738948822},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.580867350101471},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.574353039264679},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5734308958053589},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.564591109752655},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.5512201189994812},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5268755555152893},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5164933204650879},{"id":"https://openalex.org/C143141573","wikidata":"https://www.wikidata.org/wiki/Q7450971","display_name":"Sense (electronics)","level":2,"score":0.41273078322410583},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.19987517595291138},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15568271279335022},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1193644106388092},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10260340571403503},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/22m1540429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1540429","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:figshare.com:article/27805872","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:ro.uow.edu.au:test2021-15297","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22M1540429","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus Harvesting Series","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/27805872","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W563254532","https://openalex.org/W1560060148","https://openalex.org/W1575147392","https://openalex.org/W1966067080","https://openalex.org/W1978671200","https://openalex.org/W1997321092","https://openalex.org/W2017025219","https://openalex.org/W2043718735","https://openalex.org/W2062713613","https://openalex.org/W2072655083","https://openalex.org/W2087496472","https://openalex.org/W2101438312","https://openalex.org/W2106466297","https://openalex.org/W2124232799","https://openalex.org/W2154839486","https://openalex.org/W2155430897","https://openalex.org/W2174967758","https://openalex.org/W2331639718","https://openalex.org/W2333039186","https://openalex.org/W2432644127","https://openalex.org/W2912712076","https://openalex.org/W2920702560","https://openalex.org/W3100925978"],"related_works":["https://openalex.org/W57680709","https://openalex.org/W3203278930","https://openalex.org/W4302608385","https://openalex.org/W4297571134","https://openalex.org/W2983063598","https://openalex.org/W2963867164","https://openalex.org/W4297969557","https://openalex.org/W1529867338","https://openalex.org/W2230799146","https://openalex.org/W2992451487"],"abstract_inverted_index":{"We":[0],"show":[1,43],"stabilization":[2,79],"of":[3,16,33,53,67],"solutions":[4,72],"to":[5,73,86],"the":[6,14,48,51,61,77],"sixth-order":[7],"convective":[8],"Cahn-Hilliard":[9],"equation.":[10],"The":[11],"problem":[12],"has":[13,50],"structure":[15,52],"a":[17,22,57,65,82],"gradient":[18,54],"flow":[19,55],"perturbed":[20],"by":[21,37],"quadratic":[23],"destabilizing":[24],"term":[25],"with":[26],"coefficient":[27],"\\\\delta":[28,47],">":[29],"0.":[30],"Through":[31],"application":[32],"an":[34],"abstract":[35],"result":[36],"Carvalho,":[38],"Langa,":[39],"and":[40,88],"Robinson":[41],"we":[42,63],"that":[44],"for":[45,70],"small":[46],"equation":[49],"in":[56],"weak":[58],"sense.":[59],"On":[60],"way":[62],"prove":[64],"kind":[66],"Liouville":[68],"theorem":[69,84],"eternal":[71],"parabolic":[74],"problems.":[75],"Finally,":[76],"desired":[78],"follows":[80],"from":[81],"powerful":[83],"due":[85],"Hale":[87],"Raugel.":[89]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}