{"id":"https://openalex.org/W3105526842","doi":"https://doi.org/10.1137/20m1380661","title":"Constructive Exact Control of Semilinear 1D Wave Equations by a Least-Squares Approach","display_name":"Constructive Exact Control of Semilinear 1D Wave Equations by a Least-Squares Approach","publication_year":2022,"publication_date":"2022-03-07","ids":{"openalex":"https://openalex.org/W3105526842","doi":"https://doi.org/10.1137/20m1380661","mag":"3105526842"},"language":"en","primary_location":{"id":"doi:10.1137/20m1380661","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1380661","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5020369448","display_name":"Arnaud M\u00fcnch","orcid":null},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arnaud M\u00fcnch","raw_affiliation_strings":["LMBP - Laboratoire de Math\u00e9matiques Blaise Pascal (Campus universitaire des C\u00e9zeaux, 3 place Vasarely, TSA 60026 / CS 60026, 63178 Aubi\u00e8re Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMBP - Laboratoire de Math\u00e9matiques Blaise Pascal (Campus universitaire des C\u00e9zeaux, 3 place Vasarely, TSA 60026 / CS 60026, 63178 Aubi\u00e8re Cedex - France)","institution_ids":["https://openalex.org/I4210155549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089339704","display_name":"Emmanuel Tr\u00e9lat","orcid":"https://orcid.org/0000-0002-0656-7003"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuel Tr\u00e9lat","raw_affiliation_strings":["CaGE - Control And GEometry (4 place Jussieu 75005 Paris - France)","LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)"],"raw_orcid":"https://orcid.org/0000-0002-0656-7003","affiliations":[{"raw_affiliation_string":"CaGE - Control And GEometry (4 place Jussieu 75005 Paris - France)","institution_ids":[]},{"raw_affiliation_string":"LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]},{"raw_affiliation_string":"SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)","institution_ids":["https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7855,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.66091982,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"60","issue":"2","first_page":"652","last_page":"673"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.998199999332428,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.808861255645752},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5624604821205139},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5549905896186829},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5310471653938293},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5294121503829956},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5215303897857666},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.49499911069869995},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4899996817111969},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4866803288459778},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.485258549451828},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.48209908604621887},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.45590656995773315},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4461171627044678},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4253721237182617},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.4203665256500244},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40408599376678467},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.34824132919311523},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13103407621383667},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.10585552453994751},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08128625154495239}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.808861255645752},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5624604821205139},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5549905896186829},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5310471653938293},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5294121503829956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5215303897857666},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49499911069869995},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4899996817111969},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4866803288459778},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.485258549451828},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.48209908604621887},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.45590656995773315},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4461171627044678},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4253721237182617},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.4203665256500244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40408599376678467},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.34824132919311523},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13103407621383667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.10585552453994751},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08128625154495239},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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":2,"locations":[{"id":"doi:10.1137/20m1380661","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1380661","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03007045v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03007045","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2022, 60 (2), pp.652-673. ⟨10.1137/20m1380661⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6172269506","display_name":"New Trends in Control and Stabilization: Constraints and Non-local Terms","funder_award_id":"ANR-20-CE40-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6287694742","display_name":"CAP 20-25","funder_award_id":"ANR-16-IDEX-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W67237221","https://openalex.org/W1604226557","https://openalex.org/W1833425995","https://openalex.org/W1969363190","https://openalex.org/W1973697519","https://openalex.org/W2019504025","https://openalex.org/W2043124202","https://openalex.org/W2076965931","https://openalex.org/W2104082587","https://openalex.org/W2152537629","https://openalex.org/W2312961750","https://openalex.org/W2334835265","https://openalex.org/W2368776668","https://openalex.org/W2487080866","https://openalex.org/W2800444486","https://openalex.org/W3087599456","https://openalex.org/W3170378599","https://openalex.org/W3194374079","https://openalex.org/W3202839360"],"related_works":["https://openalex.org/W2954167023","https://openalex.org/W1978069580","https://openalex.org/W1964787812","https://openalex.org/W2064351239","https://openalex.org/W1970936604","https://openalex.org/W2949665548","https://openalex.org/W2053400769","https://openalex.org/W2020692468","https://openalex.org/W4376122670","https://openalex.org/W4388093492"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"proved":[3],"by":[4],"Zuazua":[5],"in":[6,28],"the":[7,10,70,90,143],"nineties":[8],"that":[9,47,99,117],"internally":[11],"controlled":[12,140],"semilinear":[13,94,144],"1D":[14,95],"wave":[15,96],"equation":[16],"$\\partial_{tt}y-\\partial_{xx}y":[17],"+":[18],"g(y)=f":[19],"1_{\\omega}$,":[20],"with":[21,31,125,148],"Dirichlet":[22],"boundary":[23],"conditions,":[24],"is":[25,119],"exactly":[26],"controllable":[27],"$H^1_0(0,1)\\cap":[29],"L^2(0,1)$":[30],"controls":[32],"$f\\in":[33],"L^2((0,1)\\times(0,T))$,":[34],"for":[35,61,89,111,142],"any":[36,39],"$T>0$":[37],"and":[38,87,116],"nonempty":[40],"open":[41],"subset":[42],"$\\omega$":[43],"of":[44,93,155],"(0,1),":[45],"assuming":[46],"$g\\in":[48],"\\mathcal{C}^1(\\mathbb{R})$":[49],"does":[50,101],"not":[51,77,102],"grow":[52,103],"faster":[53,104],"than":[54,105],"$\\beta\\vert":[55],"x\\vert":[56],"\\ln^{2}\\vert":[57,107],"x\\vert$":[58,108],"at":[59,109,146],"infinity":[60,110],"some":[62,112],"$\\beta>0$":[63,113],"small":[64,114],"enough.":[65],"The":[66],"proof,":[67],"based":[68],"on":[69,123],"Leray--Schauder":[71],"fixed":[72],"point":[73],"theorem,":[74],"is,":[75],"however,":[76],"constructive.":[78],"In":[79],"this":[80],"article,":[81],"we":[82,128],"design":[83,129],"a":[84,130,139,152],"constructive":[85],"proof":[86],"algorithm":[88,132],"exact":[91],"controllability":[92],"equations.":[97],"Assuming":[98],"$g^\\prime$":[100,118],"$\\beta":[106],"enough":[115],"uniformly":[120],"H\u00f6lder":[121],"continuous":[122],"$\\mathbb{R}$":[124],"exponent":[126],"$s\\in[0,1]$,":[127],"least-squares":[131],"yielding":[133],"an":[134],"explicit":[135],"sequence":[136],"converging":[137],"to":[138],"solution":[141],"equation,":[145],"least":[147],"order":[149],"$1+s$":[150],"after":[151],"finite":[153],"number":[154],"iterations.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}