{"id":"https://openalex.org/W2101694485","doi":"https://doi.org/10.1137/06065369x","title":"Exact Controllability of a Nonlinear Korteweg\u2013de Vries Equation on a Critical Spatial Domain","display_name":"Exact Controllability of a Nonlinear Korteweg\u2013de Vries Equation on a Critical Spatial Domain","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2101694485","doi":"https://doi.org/10.1137/06065369x","mag":"2101694485"},"language":"en","primary_location":{"id":"doi:10.1137/06065369x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065369x","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/A5025499546","display_name":"Eduardo Cerpa","orcid":"https://orcid.org/0000-0001-9974-324X"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Eduardo Cerpa","raw_affiliation_strings":["Universit\u00e9 Paris-Sud-XI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Sud-XI","institution_ids":["https://openalex.org/I102197404"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025499546"],"corresponding_institution_ids":["https://openalex.org/I102197404"],"apc_list":null,"apc_paid":null,"fwci":6.5316,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.97761366,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"46","issue":"3","first_page":"877","last_page":"899"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994000196456909,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.9438931941986084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.848405659198761},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6471074819564819},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5669059157371521},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5237172245979309},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5033454298973083},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.500769853591919},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.4536052644252777},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43519699573516846},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36571770906448364},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3336624503135681},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.19812461733818054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06042742729187012},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.059916675090789795}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.9438931941986084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.848405659198761},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6471074819564819},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5669059157371521},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5237172245979309},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5033454298973083},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.500769853591919},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.4536052644252777},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43519699573516846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36571770906448364},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3336624503135681},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.19812461733818054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06042742729187012},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.059916675090789795},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/06065369x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065369x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W46317803","https://openalex.org/W161494989","https://openalex.org/W1585954501","https://openalex.org/W1604226557","https://openalex.org/W1975993462","https://openalex.org/W1979722387","https://openalex.org/W1980366322","https://openalex.org/W1982143211","https://openalex.org/W1986788497","https://openalex.org/W1990626170","https://openalex.org/W2026967759","https://openalex.org/W2032128836","https://openalex.org/W2036831763","https://openalex.org/W2042585305","https://openalex.org/W2043585825","https://openalex.org/W2046758456","https://openalex.org/W2046933061","https://openalex.org/W2075670431","https://openalex.org/W2086519672","https://openalex.org/W2098750612","https://openalex.org/W2129842989","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2066120048","https://openalex.org/W2949745863","https://openalex.org/W3010940295","https://openalex.org/W1514481392","https://openalex.org/W2111215486","https://openalex.org/W2068031792","https://openalex.org/W2020502833","https://openalex.org/W892341692","https://openalex.org/W2100405323","https://openalex.org/W4210569427"],"abstract_inverted_index":{"We":[0,17,54],"consider":[1],"the":[2,13,31,43,57,61,66,70],"boundary":[3,15],"controllability":[4,64],"problem":[5,20],"for":[6,21,29],"a":[7,22,26,47],"nonlinear":[8,58],"Korteweg\u2013de":[9],"Vries":[10],"equation":[11],"with":[12,25,42],"Dirichlet":[14],"condition.":[16],"study":[18],"this":[19],"spatial":[23],"domain":[24],"critical":[27],"length":[28],"which":[30],"linearized":[32],"control":[33,73],"system":[34],"is":[35,74],"not":[36],"controllable.":[37],"In":[38],"order":[39],"to":[40],"deal":[41],"nonlinearity,":[44],"we":[45],"use":[46],"power":[48],"series":[49],"expansion":[50],"of":[51,72],"second":[52],"order.":[53],"prove":[55],"that":[56,69],"term":[59],"gives":[60],"local":[62],"exact":[63],"around":[65],"origin":[67],"provided":[68],"time":[71],"large":[75],"enough.":[76]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}