{"id":"https://openalex.org/W4381280347","doi":"https://doi.org/10.1093/imamci/dnad016","title":"Global exponential stabilization of the linearized Korteweg-de Vries equation with a state delay","display_name":"Global exponential stabilization of the linearized Korteweg-de Vries equation with a state delay","publication_year":2023,"publication_date":"2023-05-24","ids":{"openalex":"https://openalex.org/W4381280347","doi":"https://doi.org/10.1093/imamci/dnad016"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnad016","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnad016","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/A5066150489","display_name":"Habib Ayadi","orcid":"https://orcid.org/0000-0001-9909-8244"},"institutions":[{"id":"https://openalex.org/I55167344","display_name":"University of Kairouan","ror":"https://ror.org/024mpte60","country_code":"TN","type":"education","lineage":["https://openalex.org/I55167344"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Habib Ayadi","raw_affiliation_strings":["University of Kairouan, Higher Institute of Applied Mathematics and Computer Sciences Mathematics, , Avenue Ibn Fourat, Kairouan Sfax 3100, Tunisia"],"affiliations":[{"raw_affiliation_string":"University of Kairouan, Higher Institute of Applied Mathematics and Computer Sciences Mathematics, , Avenue Ibn Fourat, Kairouan Sfax 3100, Tunisia","institution_ids":["https://openalex.org/I55167344"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092208908","display_name":"Mariem Jlassi","orcid":null},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Mariem Jlassi","raw_affiliation_strings":["University of Sfax, Faculty of Sciences Mathematics, , Soukra Road, Km 4, Kairouan Sfax 3000, Tunisia"],"affiliations":[{"raw_affiliation_string":"University of Sfax, Faculty of Sciences Mathematics, , Soukra Road, Km 4, Kairouan Sfax 3000, Tunisia","institution_ids":["https://openalex.org/I142899784"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066150489"],"corresponding_institution_ids":["https://openalex.org/I55167344"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":0.3756,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57325361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"40","issue":"3","first_page":"516","last_page":"533"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9896000027656555,"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/mathematics","display_name":"Mathematics","score":0.7670613527297974},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.6939359903335571},{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.6321202516555786},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5509372353553772},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.525784969329834},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4696109890937805},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4629190266132355},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.43772774934768677},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4178315997123718},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.37099865078926086},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3670744001865387},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.23854830861091614},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.12236317992210388},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12061551213264465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0976613461971283},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07706081867218018}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7670613527297974},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.6939359903335571},{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.6321202516555786},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5509372353553772},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.525784969329834},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4696109890937805},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4629190266132355},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.43772774934768677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4178315997123718},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.37099865078926086},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3670744001865387},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.23854830861091614},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.12236317992210388},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12061551213264465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0976613461971283},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07706081867218018},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnad016","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnad016","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W251471563","https://openalex.org/W393289797","https://openalex.org/W1527296550","https://openalex.org/W1795303450","https://openalex.org/W1972257629","https://openalex.org/W1977315171","https://openalex.org/W1979722387","https://openalex.org/W1980351610","https://openalex.org/W1990834167","https://openalex.org/W1998462963","https://openalex.org/W2000695677","https://openalex.org/W2001173127","https://openalex.org/W2021731075","https://openalex.org/W2026967759","https://openalex.org/W2054263590","https://openalex.org/W2056522232","https://openalex.org/W2075215365","https://openalex.org/W2088779465","https://openalex.org/W2146588488","https://openalex.org/W2161450707","https://openalex.org/W2166801103","https://openalex.org/W2172250835","https://openalex.org/W2499641798","https://openalex.org/W2522650499","https://openalex.org/W2540877599","https://openalex.org/W2544978468","https://openalex.org/W2731013142","https://openalex.org/W2765520046","https://openalex.org/W2793667768","https://openalex.org/W2902661488","https://openalex.org/W2963562890","https://openalex.org/W2986929701","https://openalex.org/W3094142253","https://openalex.org/W3170731810","https://openalex.org/W4211202937","https://openalex.org/W4365806539","https://openalex.org/W6628936366","https://openalex.org/W6638063026","https://openalex.org/W6640436295","https://openalex.org/W6642226493","https://openalex.org/W6649949206","https://openalex.org/W6675599905","https://openalex.org/W6696213706"],"related_works":["https://openalex.org/W2771027241","https://openalex.org/W1765905465","https://openalex.org/W2793080664","https://openalex.org/W2186140227","https://openalex.org/W2132535444","https://openalex.org/W2534185822","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,73],"paper,":[3],"well-posedness":[4,78],"and":[5,32,64,88],"global":[6],"boundary":[7,37],"exponential":[8,90,116],"stabilization":[9,91],"problems":[10],"are":[11],"studied":[12],"for":[13,47,118],"the":[14,35,43,48,57,77,80,93,99,108,114,119,130],"one-dimensional":[15],"linearized":[16],"Korteweg-de":[17],"Vries":[18],"equation":[19],"(KdV)":[20],"with":[21],"state":[22],"delay,":[23],"which":[24],"is":[25,70,126],"posed":[26],"in":[27,83,92],"bounded":[28],"interval":[29],"$[0,2\\pi":[30],"]$":[31],"actuated":[33],"at":[34],"left":[36],"by":[38,98],"Dirichlet":[39],"condition.":[40],"Based":[41],"on":[42],"infinite-dimensional":[44],"backstepping":[45],"method":[46],"delay-free":[49],"case,":[50],"a":[51],"linear":[52],"Volterra-type":[53],"integral":[54],"transformation":[55],"maps":[56],"system":[58,82],"into":[59],"another":[60],"homogeneous":[61],"target":[62],"system,":[63],"an":[65,84,102],"explicit":[66],"feedback":[67,110],"control":[68],"law":[69],"obtained.":[71],"Under":[72],"feedback,":[74],"we":[75,112],"prove":[76],"of":[79,95,101],"considered":[81],"appropriate":[85,103],"Banach":[86],"space":[87],"its":[89],"topology":[94],"$L^{2}(0,2\\pi":[96],")$-norm":[97],"use":[100],"Lyapunov\u2013Razumikhin":[104],"functional.":[105],"Moreover,":[106],"under":[107],"same":[109],"law,":[111],"get":[113],"local":[115],"stability":[117],"non-linear":[120],"KdV":[121],"equation.":[122],"A":[123],"numerical":[124],"example":[125],"provided":[127],"to":[128],"illustrate":[129],"result.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
