{"id":"https://openalex.org/W2995186665","doi":"https://doi.org/10.1109/tac.2019.2960272","title":"Singular Perturbation Analysis of a Coupled System Involving the Wave Equation","display_name":"Singular Perturbation Analysis of a Coupled System Involving the Wave Equation","publication_year":2019,"publication_date":"2019-12-17","ids":{"openalex":"https://openalex.org/W2995186665","doi":"https://doi.org/10.1109/tac.2019.2960272","mag":"2995186665"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2019.2960272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2960272","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03066813","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025499546","display_name":"Eduardo Cerpa","orcid":"https://orcid.org/0000-0001-9974-324X"},"institutions":[{"id":"https://openalex.org/I75778554","display_name":"Federico Santa Mar\u00eda Technical University","ror":"https://ror.org/05510vn56","country_code":"CL","type":"education","lineage":["https://openalex.org/I75778554"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Eduardo Cerpa","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Av. Espa\u00f1a, Chile","Universidad Tecnica Federico Santa Maria [Valparaiso]"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Av. Espa\u00f1a, Chile","institution_ids":["https://openalex.org/I75778554"]},{"raw_affiliation_string":"Universidad Tecnica Federico Santa Maria [Valparaiso]","institution_ids":["https://openalex.org/I75778554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083387069","display_name":"Christophe Prieur","orcid":"https://orcid.org/0000-0002-4456-2019"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Prieur","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, Grenoble, France","GIPSA - Infinite Dimensional Dynamics"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"GIPSA - Infinite Dimensional Dynamics","institution_ids":["https://openalex.org/I4210124956"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025499546"],"corresponding_institution_ids":["https://openalex.org/I75778554"],"apc_list":null,"apc_paid":null,"fwci":0.674,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.71784448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"65","issue":"11","first_page":"4846","last_page":"4853"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.6503514647483826},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6061467528343201},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5908248424530029},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.5741814374923706},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5638855695724487},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.558966338634491},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5388097763061523},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.49327582120895386},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4687604606151581},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4354555606842041},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3398047089576721},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2254597544670105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19666555523872375},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.1129743754863739}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.6503514647483826},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6061467528343201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5908248424530029},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5741814374923706},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5638855695724487},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.558966338634491},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5388097763061523},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.49327582120895386},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4687604606151581},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4354555606842041},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3398047089576721},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2254597544670105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19666555523872375},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.1129743754863739},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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":2,"locations":[{"id":"doi:10.1109/tac.2019.2960272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2960272","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03066813v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03066813","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2020, 65 (11), pp.4846-4853. ⟨10.1109/TAC.2019.2960272⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03066813v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03066813","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2020, 65 (11), pp.4846-4853. ⟨10.1109/TAC.2019.2960272⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W564609686","https://openalex.org/W1499647655","https://openalex.org/W1964647016","https://openalex.org/W1974777461","https://openalex.org/W1974790392","https://openalex.org/W2040805915","https://openalex.org/W2043120443","https://openalex.org/W2053963271","https://openalex.org/W2057432879","https://openalex.org/W2086234688","https://openalex.org/W2110837625","https://openalex.org/W2120748789","https://openalex.org/W2162356143","https://openalex.org/W2280036388","https://openalex.org/W2482021336","https://openalex.org/W2585071366","https://openalex.org/W2727537826","https://openalex.org/W2740763313","https://openalex.org/W2780413159","https://openalex.org/W2785675571","https://openalex.org/W3102398605","https://openalex.org/W3124026823","https://openalex.org/W4298348076","https://openalex.org/W6843904563"],"related_works":["https://openalex.org/W2533995846","https://openalex.org/W3131586246","https://openalex.org/W2999616507","https://openalex.org/W2125893105","https://openalex.org/W1994904484","https://openalex.org/W2012779601","https://openalex.org/W4392238179","https://openalex.org/W3164276969","https://openalex.org/W2946027129","https://openalex.org/W3201990513"],"abstract_inverted_index":{"This":[0],"article":[1],"considers":[2],"a":[3,11,21,29,40,126],"system":[4,51,91,112,124],"coupling":[5],"an":[6],"ordinary":[7],"differential":[8],"equation":[9,13,27],"with":[10],"wave":[12,26,140],"through":[14],"its":[15],"boundary":[16],"data.":[17],"The":[18],"existence":[19],"of":[20,38,48,56,85,88,122,133,149],"small":[22],"parameter":[23],"in":[24,72],"the":[25,32,36,46,49,54,62,86,89,94,105,111,120,123,131,139,147],"(as":[28],"factor":[30],"multiplying":[31],"time":[33],"derivative)":[34],"suggests":[35],"idea":[37],"applying":[39],"singular":[41,106],"perturbation":[42,107],"method":[43,76,108],"to":[44,145],"get":[45,119],"stability":[47,55,87,121],"full":[50,90],"by":[52,61],"analyzing":[53],"some":[57,73],"appropriate":[58],"subsystems":[59,96],"given":[60,95],"method.":[63],"However,":[64],"for":[65,110,136],"infinite-dimensional":[66],"systems,":[67],"it":[68],"is":[69,130],"known":[70],"that":[71,104],"cases,":[74],"this":[75,100,116,134],"does":[77],"not":[78],"work.":[79],"Indeed,":[80],"one":[81],"cannot":[82],"be":[83],"sure":[84],"even":[92],"if":[93],"are":[97,143],"stable.":[98],"In":[99],"article,":[101],"we":[102,118],"prove":[103],"works":[109],"under":[113],"study.":[114],"Using":[115],"strategy,":[117],"and":[125],"Tikhonov":[127],"theorem,":[128],"which":[129],"first":[132],"kind":[135],"systems":[137],"involving":[138],"equation.":[141],"Simulations":[142],"performed":[144],"show":[146],"applicability":[148],"our":[150],"results.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}