{"id":"https://openalex.org/W2044803201","doi":"https://doi.org/10.1137/050647281","title":"Synchronization of a Stochastic Reaction\u2010Diffusion System on a Thin Two\u2010Layer Domain","display_name":"Synchronization of a Stochastic Reaction\u2010Diffusion System on a Thin Two\u2010Layer Domain","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2044803201","doi":"https://doi.org/10.1137/050647281","mag":"2044803201"},"language":"en","primary_location":{"id":"doi:10.1137/050647281","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647281","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/A5085582592","display_name":"Tom\u00e1s Caraballo","orcid":"https://orcid.org/0000-0003-4697-898X"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Tom\u00e1s Caraballo","raw_affiliation_strings":["Departamento Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025334898","display_name":"Igor \u010chue\u0161hov","orcid":"https://orcid.org/0000-0001-8793-8752"},"institutions":[{"id":"https://openalex.org/I8765205","display_name":"V. N. Karazin Kharkiv National University","ror":"https://ror.org/03ftejk10","country_code":"UA","type":"education","lineage":["https://openalex.org/I8765205"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Igor D. Chueshov","raw_affiliation_strings":["Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody sq., 61077, Kharkov, Ukraine"],"affiliations":[{"raw_affiliation_string":"Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody sq., 61077, Kharkov, Ukraine","institution_ids":["https://openalex.org/I8765205"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021471659","display_name":"Peter E. Kloeden","orcid":"https://orcid.org/0000-0001-9505-2257"},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter E. Kloeden","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Johann Wolfgang Goethe-Universit\u00e4t, D-60054 Frankfurt am Main, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Johann Wolfgang Goethe-Universit\u00e4t, D-60054 Frankfurt am Main, Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085582592"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"apc_list":null,"apc_paid":null,"fwci":7.0338,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.96530182,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"38","issue":"5","first_page":"1489","last_page":"1507"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"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":0.9843000173568726,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7162907123565674},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.54010409116745},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.5392280220985413},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5213583707809448},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5050471425056458},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4680713415145874},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4635917544364929},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.12241709232330322},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08215558528900146}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7162907123565674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.54010409116745},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.5392280220985413},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5213583707809448},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5050471425056458},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4680713415145874},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4635917544364929},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.12241709232330322},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08215558528900146},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050647281","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647281","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:dnet:idus________::ccb0931a7321eed4e7d6bfd7c8e03d34","is_oa":false,"landing_page_url":"https://idus.us.es/handle/11441/23719","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W137556955","https://openalex.org/W1585299400","https://openalex.org/W1802196594","https://openalex.org/W1967374925","https://openalex.org/W1988538595","https://openalex.org/W2014884866","https://openalex.org/W2018697994","https://openalex.org/W2023590249","https://openalex.org/W2030634487","https://openalex.org/W2061075223","https://openalex.org/W2066976366","https://openalex.org/W2070430318","https://openalex.org/W2107905501","https://openalex.org/W2132991104","https://openalex.org/W4250087930"],"related_works":["https://openalex.org/W4294364856","https://openalex.org/W2164522043","https://openalex.org/W2315570462","https://openalex.org/W2299552569","https://openalex.org/W4383216082","https://openalex.org/W4377164417","https://openalex.org/W2163912400","https://openalex.org/W4298018575","https://openalex.org/W2700088093","https://openalex.org/W2359419821"],"abstract_inverted_index":{"A":[0],"system":[1],"of":[2,18,111,122,169,175,184],"semilinear":[3],"parabolic":[4,154],"stochastic":[5,153],"partial":[6],"differential":[7],"equations":[8,37],"with":[9,58,156,194],"additive":[10,71],"space\u2010time":[11,72],"noise":[12,99,186],"is":[13,100,148],"considered":[14],"on":[15,44,78,88,172],"the":[16,28,79,89,94,98,101,112,119,123,130,136,140,145,157,170,176,182,198],"union":[17],"thin":[19,95],"bounded":[20],"tubular":[21],"domains":[22],"$D_{1,\\eps}:=\\Gamma\\times(0,\\eps)$":[23],"and":[24,62,86,107,161,205],"$D_{2,\\eps}:=\\Gamma\\times(-\\eps,0)$":[25],"joined":[26],"at":[27],"common":[29,177],"base":[30,80,178],"$\\Gamma":[31],"\\subset":[32],"{\\R}^{d}$,":[33],"where":[34,52],"$d\\ge1$.":[35],"The":[36],"are":[38,68,116],"coupled":[39],"by":[40,150,203],"an":[41],"interface":[42],"condition":[43],"$\\Gamma$":[45],"which":[46,75,165],"involves":[47],"a":[48,151,162],"reaction":[49],"intensity":[50,137],"$k(x',\\eps)$,":[51],"$x":[53],"=":[54],"(x',x_{d+1})":[55],"\\in":[56,60,84],"\\mathbb{R}^{d+1}$":[57],"$x'":[59,83],"\\Gamma$":[61,85],"$|x_{d+1}|":[63],"<":[64],"\\eps$.":[65],"Random":[66],"influences":[67],"included":[69],"through":[70],"Brownian":[73],"motion,":[74],"depend":[76],"only":[77],"spatial":[81,90],"variable":[82,91],"not":[87],"$x_{d+1}$":[92],"in":[93,103,181,192,197],"direction.":[96],"Moreover,":[97,180],"same":[102],"both":[104,173],"layers":[105],"$D_{1,\\eps}$":[106],"$D_{2,\\eps}$.":[108],"Limiting":[109],"properties":[110],"global":[113],"random":[114],"attractor":[115],"established":[117],"as":[118,129],"thinness":[120],"parameter":[121],"domain":[124,132],"$\\eps":[125],"\\to":[126],"0$,":[127],"i.e.,":[128],"initial":[131],"becomes":[133],"thinner,":[134],"when":[135],"function":[138],"possesses":[139],"property":[141],"$\\lim_{\\eps\\to0}\\eps^{-1}k(x',\\eps)=+\\infty$.":[142],"In":[143],"particular,":[144],"limiting":[146],"dynamics":[147,171],"described":[149],"single":[152],"equation":[155],"averaged":[158],"diffusion":[159],"coefficient":[160],"nonlinearity":[163],"term,":[164],"essentially":[166],"indicates":[167],"synchronization":[168,190],"sides":[174],"$\\Gamma$.":[179],"case":[183,200],"nondegenerate":[185],"we":[187],"obtain":[188],"stronger":[189],"phenomena":[191],"comparison":[193],"analogous":[195],"results":[196],"deterministic":[199],"previously":[201],"investigated":[202],"Chueshov":[204],"Rekalo":[206],"[EQUADIFF\u20102003,":[207],"F.":[208],"Dumortier":[209],"et":[210],"al.,":[211],"eds.,":[212],"World":[213],"Scientific,":[214],"Hackensack,":[215],"NJ,":[216],"2005,":[217],"pp.":[218,224],"645\u2013650;":[219],"Sb.":[220],"Math.,":[221],"195":[222],"(2004),":[223],"103\u2013128].":[225]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}