{"id":"https://openalex.org/W1782059086","doi":"https://doi.org/10.3233/asy-2012-1116","title":"On homogenization of nonlinear Robin type boundary conditions for cavities along manifolds and associated spectral problems","display_name":"On homogenization of nonlinear Robin type boundary conditions for cavities along manifolds and associated spectral problems","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W1782059086","doi":"https://doi.org/10.3233/asy-2012-1116","mag":"1782059086"},"language":"en","primary_location":{"id":"doi:10.3233/asy-2012-1116","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2012-1116","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic 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/A5065345616","display_name":"Delfina G\u00f3mez","orcid":"https://orcid.org/0000-0002-8791-7684"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"D. G\u00f3mez","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Estad\u00edstica y Computaci\u00f3n, Universidad de Cantabria, Santander, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Estad\u00edstica y Computaci\u00f3n, Universidad de Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112763288","display_name":"E. P\u00e9rez","orcid":null},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E. P\u00e9rez","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, Universidad de Cantabria, Santander, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, Universidad de Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034554661","display_name":"\u0422. \u0410. \u0428\u0430\u043f\u043e\u0448\u043d\u0438\u043a\u043e\u0432\u0430","orcid":"https://orcid.org/0000-0003-1865-0223"},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"T.A. Shaposhnikova","raw_affiliation_strings":["Department of Differential Equations, Moscow State University, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Differential Equations, Moscow State University, Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065345616"],"corresponding_institution_ids":["https://openalex.org/I13134134"],"apc_list":null,"apc_paid":null,"fwci":2.7768,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.90011723,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"80","issue":"3-4","first_page":"289","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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/T11558","display_name":"Composite Material Mechanics","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8967111706733704},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6545693874359131},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.5173794031143188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47445592284202576},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4704191982746124},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4332853853702545},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4145764112472534},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.3414844870567322},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2325919270515442},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.15659385919570923}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8967111706733704},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6545693874359131},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.5173794031143188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47445592284202576},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4704191982746124},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4332853853702545},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4145764112472534},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.3414844870567322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2325919270515442},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.15659385919570923},{"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/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/asy-2012-1116","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2012-1116","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W243770149","https://openalex.org/W623322177","https://openalex.org/W650857255","https://openalex.org/W1517403807","https://openalex.org/W1572320440","https://openalex.org/W1614394106","https://openalex.org/W1963914393","https://openalex.org/W1995970852","https://openalex.org/W1999866447","https://openalex.org/W2043997170","https://openalex.org/W2054068484","https://openalex.org/W2069882400","https://openalex.org/W2103437628","https://openalex.org/W2142209297","https://openalex.org/W2225962153","https://openalex.org/W2499030322","https://openalex.org/W3091814460"],"related_works":["https://openalex.org/W2020502833","https://openalex.org/W2947472662","https://openalex.org/W4288364258","https://openalex.org/W2989875570","https://openalex.org/W2746742617","https://openalex.org/W2884266624","https://openalex.org/W3021583104","https://openalex.org/W1976461178","https://openalex.org/W2945950509","https://openalex.org/W2102336248"],"abstract_inverted_index":{"Let":[0],"u":[1,163],"\u03b5":[2,38,164],"be":[3],"the":[4,7,29,56,69,72,87,99,104,110,131,148,160,166,191,194,199],"solution":[5],"of":[6,51,74,106,130,147,162,169,181,193,201],"Poisson":[8],"equation":[9],"in":[10,165,198],"a":[11,16,22,42,49,91,119,127,144,203],"domain":[12,50],"periodically":[13],"perforated":[14],"along":[15],"manifold":[17],"\u03b3=\u03a9\u2229{x":[18],"1":[19,93,171],"=0},":[20],"with":[21,41,54,81],"nonlinear":[23,88],"Robin":[24],"type":[25],"boundary":[26],"condition":[27,44],"on":[28,45,103,113,133,152],"perforations":[30],"(the":[31],"flux":[32],"here":[33],"being":[34],"O(\u03b5":[35,78],"\u2212\u03ba":[36],")\u03c3(x,u":[37],")),":[39],"and":[40,71,98,108,172],"Dirichlet":[43],"\u2202\u03a9.":[46],"\u03a9":[47],"is":[48,77,90,154],"R":[52],"n":[53,153],"n\u22653,":[55],"small":[57],"parameter":[58,100],"\u03b5,":[59],"that":[60],"we":[61,117,158],"shall":[62],"make":[63],"to":[64,66,138,187],"go":[65],"zero,":[67],"denotes":[68],"period,":[70],"size":[73,146],"each":[75,141],"cavity":[76],"\u03b1":[79,107],")":[80],"\u03b1\u22651.":[82],"The":[83],"function":[84,97],"\u03c3":[85,202],"involving":[86],"process":[89,132],"C":[92],"(\u03a9":[94],"\u00af":[95],"\u00d7R)":[96],"\u03ba\u2208R.":[101],"Depending":[102],"values":[105],"\u03ba,":[109],"effective":[111],"equations":[112],"\u03b3":[114,134],"are":[115],"obtained;":[116],"provide":[118,176],"critical":[120,145],"relation":[121],"between":[122],"both":[123],"parameters":[124],"which":[125,150,175],"implies":[126],"different":[128],"average":[129],"ranging":[135],"from":[136],"linear":[137,204],"nonlinear.":[139],"For":[140],"fixed":[142],"\u03ba":[143],"cavities":[149],"depends":[151],"found.":[155],"As":[156],"\u03b5\u21920,":[157],"show":[159],"convergence":[161,179,189],"weak":[167],"topology":[168],"H":[170],"construct":[173],"correctors":[174],"estimates":[177],"for":[178,190],"rates":[180],"solutions.":[182],"All":[183],"this":[184],"allows":[185],"us":[186],"derive":[188],"eigenelements":[192],"associated":[195],"spectral":[196],"problems":[197],"case":[200],"function.":[205]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-30T06:05:26.967640","created_date":"2025-10-10T00:00:00"}
