{"id":"https://openalex.org/W2155430897","doi":"https://doi.org/10.1137/110834123","title":"On a Higher Order Convective Cahn--Hilliard-Type Equation","display_name":"On a Higher Order Convective Cahn--Hilliard-Type Equation","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2155430897","doi":"https://doi.org/10.1137/110834123","mag":"2155430897"},"language":"en","primary_location":{"id":"doi:10.1137/110834123","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110834123","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5017707470","display_name":"M. D. Korzec","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. D. Korzec","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019510066","display_name":"Piotr Rybka","orcid":"https://orcid.org/0000-0002-0694-8201"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Rybka","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017707470"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6605,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.84126542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"72","issue":"4","first_page":"1343","last_page":"1360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9990000128746033,"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":0.9990000128746033,"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/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9955000281333923,"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/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.8602740168571472},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6437810063362122},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5874887704849243},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5408161282539368},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5332351326942444},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.529968798160553},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5062219500541687},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4588315188884735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4494277834892273},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4399341344833374},{"id":"https://openalex.org/keywords/deposition","display_name":"Deposition (geology)","score":0.4398972690105438},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.43350598216056824},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32129818201065063},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2807758152484894},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.2154616415500641},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11684489250183105}],"concepts":[{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.8602740168571472},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6437810063362122},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5874887704849243},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5408161282539368},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5332351326942444},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.529968798160553},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5062219500541687},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4588315188884735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4494277834892273},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4399341344833374},{"id":"https://openalex.org/C64297162","wikidata":"https://www.wikidata.org/wiki/Q1987070","display_name":"Deposition (geology)","level":3,"score":0.4398972690105438},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.43350598216056824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32129818201065063},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2807758152484894},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2154616415500641},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11684489250183105},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C2816523","wikidata":"https://www.wikidata.org/wiki/Q180184","display_name":"Sediment","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110834123","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110834123","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:doi:10.20347/wias.preprint.1582","is_oa":false,"landing_page_url":"http://localhost:8291/receive/wias_mods_00002923","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"preprint"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1985907546","https://openalex.org/W2003205185","https://openalex.org/W2017334281","https://openalex.org/W2019262765","https://openalex.org/W2037933894","https://openalex.org/W2041832550","https://openalex.org/W2043466506","https://openalex.org/W2047182178","https://openalex.org/W2062713613","https://openalex.org/W2064274222","https://openalex.org/W2072655083","https://openalex.org/W2075085615","https://openalex.org/W2079944289","https://openalex.org/W2081968584","https://openalex.org/W2082261293","https://openalex.org/W2107877854","https://openalex.org/W2124232799","https://openalex.org/W2165247671","https://openalex.org/W2169920821","https://openalex.org/W2317462844","https://openalex.org/W2483043382","https://openalex.org/W3100925978"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W62102365"],"abstract_inverted_index":{"A":[0,88],"higher":[1],"order":[2,33],"convective":[3],"Cahn--Hilliard-type":[4],"equation":[5,36],"that":[6,61],"describes":[7],"the":[8,25,54,62],"faceting":[9],"of":[10,27,53],"a":[11,22,57,76],"growing":[12],"surface":[13],"is":[14,37],"considered":[15],"with":[16,94],"periodic":[17],"boundary":[18],"conditions.":[19],"By":[20],"using":[21],"Galerkin":[23],"approach,":[24],"existence":[26],"weak":[28],"solutions":[29],"to":[30,50,66,69,82],"this":[31],"sixth":[32],"partial":[34],"differential":[35],"established":[38],"in":[39,75],"$L^2(0,T;\\dot{H}^3_{per})$.":[40],"Additionally,":[41],"stronger":[42],"regularity":[43],"results":[44],"are":[45,48],"derived.":[46],"These":[47],"used":[49],"prove":[51],"uniqueness":[52],"solutions.":[55],"Furthermore":[56],"numerical":[58],"study":[59],"shows":[60],"transition":[63],"from":[64],"coarsening":[65],"roughening":[67],"leads":[68],"multidomain-wall":[70],"stationary":[71],"and":[72,81],"traveling":[73],"states":[74],"small":[77],"deposition":[78,96],"rate":[79],"regime":[80],"chaotic":[83],"surfaces":[84],"for":[85],"increased":[86],"rates.":[87],"characteristic":[89],"length":[90],"scale":[91],"decreases":[92],"logarithmically":[93],"increasing":[95],"rate.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
