{"id":"https://openalex.org/W2048884404","doi":"https://doi.org/10.1137/130925517","title":"Relaxation to Equilibrium in the One-Dimensional Cahn--Hilliard Equation","display_name":"Relaxation to Equilibrium in the One-Dimensional Cahn--Hilliard Equation","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2048884404","doi":"https://doi.org/10.1137/130925517","mag":"2048884404"},"language":"en","primary_location":{"id":"doi:10.1137/130925517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130925517","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/A5073872018","display_name":"F\u00e9lix Otto","orcid":"https://orcid.org/0000-0002-2327-5950"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Felix Otto","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001701382","display_name":"Maria G. Westdickenberg","orcid":"https://orcid.org/0000-0003-4342-4375"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maria G. Westdickenberg","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073872018"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0968,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.78371157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"46","issue":"1","first_page":"720","last_page":"756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7247194051742554},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7140529155731201},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6060886979103088},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.5882685780525208},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.586686372756958},{"id":"https://openalex.org/keywords/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.575478732585907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5581701397895813},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5364091992378235},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.4975018799304962},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4910249710083008},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4432763159275055},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4403364658355713},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.35773229598999023},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29206734895706177},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2421962022781372},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11040562391281128}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7247194051742554},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7140529155731201},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6060886979103088},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.5882685780525208},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.586686372756958},{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.575478732585907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5581701397895813},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5364091992378235},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.4975018799304962},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4910249710083008},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4432763159275055},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4403364658355713},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.35773229598999023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29206734895706177},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2421962022781372},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11040562391281128},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130925517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130925517","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:edoc.mpg.de:708517","is_oa":false,"landing_page_url":"http://edoc.mpg.de/708517","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"SIAM Journal on Mathematical Analysis, v.46, 720-756 (2014)","raw_type":"Article"},{"id":"pmh:oai:publications.rwth-aachen.de:235012","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/235012","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on mathematical analysis 46(1), 720-756 (2014). doi:10.1137/130925517","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W254675422","https://openalex.org/W1582617215","https://openalex.org/W1649261177","https://openalex.org/W1986608418","https://openalex.org/W1993898214","https://openalex.org/W2004567947","https://openalex.org/W2010423226","https://openalex.org/W2031170306","https://openalex.org/W2034879619","https://openalex.org/W2048619241","https://openalex.org/W2066476818","https://openalex.org/W2070854404","https://openalex.org/W2071261369","https://openalex.org/W2083530469","https://openalex.org/W2104027001","https://openalex.org/W2135756860","https://openalex.org/W2972127450","https://openalex.org/W3102578808"],"related_works":["https://openalex.org/W57680709","https://openalex.org/W159838764","https://openalex.org/W3203278930","https://openalex.org/W4385473842","https://openalex.org/W4302608385","https://openalex.org/W4297571134","https://openalex.org/W2983063598","https://openalex.org/W2963867164","https://openalex.org/W4297969557","https://openalex.org/W1529867338"],"abstract_inverted_index":{"We":[0,18],"study":[1],"the":[2,10,15,23,28,31,39,46,57,63,91,93,96,103,112,116,119,137],"stability":[3],"of":[4,41,115,118,136],"a":[5,42,51,66,100,141],"so-called":[6],"kink":[7,43,52],"profile":[8],"for":[9],"one-dimensional":[11],"Cahn--Hilliard":[12],"problem":[13],"on":[14,22],"real":[16],"line.":[17],"derive":[19],"optimal":[20],"bounds":[21],"decay":[24],"to":[25,50,71,78,99,110,140],"equilibrium":[26],"under":[27],"assumption":[29],"that":[30,45],"initial":[32,47,138],"energy":[33,40],"is":[34,53,60,65,77,106,125],"less":[35],"than":[36],"three":[37,88],"times":[38],"and":[44,80,84,95,108],"$\\dot{H}^{-1}$":[48,58,97],"distance":[49,59,98,139],"bounded.":[54],"Working":[55],"with":[56,69],"natural,":[61],"since":[62],"equation":[64],"gradient":[67],"flow":[68],"respect":[70],"this":[72],"metric.":[73],"Indeed,":[74],"our":[75],"method":[76],"establish":[79],"exploit":[81],"elementary":[82],"algebraic":[83],"differential":[85],"relationships":[86],"among":[87],"natural":[89],"quantities:":[90],"energy,":[92],"dissipation,":[94],"kink.":[101,122],"Along":[102],"way":[104],"it":[105],"necessary":[107],"possible":[109],"control":[111],"time-dependent":[113],"shift":[114],"center":[117],"$L^2$":[120],"closest":[121],"Our":[123],"result":[124],"different":[126],"from":[127],"earlier":[128],"results":[129],"because":[130],"we":[131,143],"do":[132],"not":[133],"assume":[134,144],"smallness":[135],"kink;":[142],"only":[145],"boundedness.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
