{"id":"https://openalex.org/W2521163219","doi":"https://doi.org/10.1137/16m1061837","title":"Global Stabilization of a Korteweg--De Vries Equation With Saturating Distributed Control","display_name":"Global Stabilization of a Korteweg--De Vries Equation With Saturating Distributed Control","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2521163219","doi":"https://doi.org/10.1137/16m1061837","mag":"2521163219"},"language":"en","primary_location":{"id":"doi:10.1137/16m1061837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1061837","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1609.05728","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043449102","display_name":"Swann Marx","orcid":"https://orcid.org/0000-0002-0722-3560"},"institutions":[{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","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"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Swann Marx","raw_affiliation_strings":["GIPSA-SYSCO - GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9 (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"GIPSA-SYSCO - GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9 (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","institution_ids":["https://openalex.org/I4210124956"]}]},{"author_position":"middle","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":false,"raw_author_name":"Eduardo Cerpa","raw_affiliation_strings":["UTFSM - Universidad Tecnica Federico Santa Maria [Valparaiso] (Avenida Espa\u00f1a 1680, Valpara\u00edso - Chile)"],"affiliations":[{"raw_affiliation_string":"UTFSM - Universidad Tecnica Federico Santa Maria [Valparaiso] (Avenida Espa\u00f1a 1680, Valpara\u00edso - Chile)","institution_ids":["https://openalex.org/I75778554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083387069","display_name":"Christophe Prieur","orcid":"https://orcid.org/0000-0002-4456-2019"},"institutions":[{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Prieur","raw_affiliation_strings":["GIPSA-SYSCO - GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9 (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"GIPSA-SYSCO - GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9 (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","institution_ids":["https://openalex.org/I4210124956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082790000","display_name":"Vincent Andrieu","orcid":"https://orcid.org/0000-0003-1877-6205"},"institutions":[{"id":"https://openalex.org/I4210143168","display_name":"Automation and Process Engineering Laboratory","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]},{"id":"https://openalex.org/I59692284","display_name":"\u00c9cole d'Ing\u00e9nieurs en Chimie et Sciences du Num\u00e9rique","ror":"https://ror.org/01cbtr271","country_code":"FR","type":"education","lineage":["https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Andrieu","raw_affiliation_strings":["LAGEP - Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s (b\u00e2t 308G ESCPE-Lyon, 2\u00e8me \u00e9tage 43 bd du 11 Novembre 1918 69622 Villeurbanne Cedex - France)"],"affiliations":[{"raw_affiliation_string":"LAGEP - Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s (b\u00e2t 308G ESCPE-Lyon, 2\u00e8me \u00e9tage 43 bd du 11 Novembre 1918 69622 Villeurbanne Cedex - France)","institution_ids":["https://openalex.org/I4210143168","https://openalex.org/I59692284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043449102"],"corresponding_institution_ids":["https://openalex.org/I4210124956"],"apc_list":null,"apc_paid":null,"fwci":8.6978,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.98661979,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"55","issue":"3","first_page":"1452","last_page":"1480"},"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":0.9991999864578247,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.6635032892227173},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5601614713668823},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5595217943191528},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5302984714508057},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.526982307434082},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5087462067604065},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4657144546508789},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.45620155334472656},{"id":"https://openalex.org/keywords/stability-theorem","display_name":"Stability theorem","score":0.44781729578971863},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.4309979975223541},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17220094799995422}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6635032892227173},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5601614713668823},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5595217943191528},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5302984714508057},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.526982307434082},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5087462067604065},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4657144546508789},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.45620155334472656},{"id":"https://openalex.org/C2985318062","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theorem","level":3,"score":0.44781729578971863},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.4309979975223541},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17220094799995422},{"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/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"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":3,"locations":[{"id":"doi:10.1137/16m1061837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1061837","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:arXiv.org:1609.05728","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.05728","pdf_url":"https://arxiv.org/pdf/1609.05728","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01367622v3","is_oa":true,"landing_page_url":"https://hal.science/hal-01367622","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":"http://epubs.siam.org/doi/abs/10.1137/16M1061837","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1609.05728","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.05728","pdf_url":"https://arxiv.org/pdf/1609.05728","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/6","score":0.7900000214576721,"display_name":"Clean water and sanitation"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W46317803","https://openalex.org/W1961945912","https://openalex.org/W1970596682","https://openalex.org/W1971004260","https://openalex.org/W1980351610","https://openalex.org/W1980366322","https://openalex.org/W1985982935","https://openalex.org/W1988511271","https://openalex.org/W1996311525","https://openalex.org/W2024081271","https://openalex.org/W2026967759","https://openalex.org/W2034024496","https://openalex.org/W2035475156","https://openalex.org/W2037672885","https://openalex.org/W2042518967","https://openalex.org/W2043120443","https://openalex.org/W2046142489","https://openalex.org/W2051203494","https://openalex.org/W2066888772","https://openalex.org/W2071690997","https://openalex.org/W2073078790","https://openalex.org/W2084749319","https://openalex.org/W2086519672","https://openalex.org/W2091019995","https://openalex.org/W2114920878","https://openalex.org/W2134472078","https://openalex.org/W2142435133","https://openalex.org/W2157127092","https://openalex.org/W2344666630","https://openalex.org/W2541681687"],"related_works":["https://openalex.org/W2027202866","https://openalex.org/W3149920197","https://openalex.org/W4293569346","https://openalex.org/W2302683464","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590","https://openalex.org/W849253280","https://openalex.org/W2045381003"],"abstract_inverted_index":{"This":[0],"article":[1],"deals":[2],"with":[3,93],"the":[4,10,62,68,72,82,87,98,106,110,122,125],"design":[5],"of":[6,12,29,38,55,61,67,71,124],"saturated":[7,39],"controls":[8,40],"in":[9,77],"context":[11],"partial":[13,128],"differential":[14,129],"equations.":[15],"It":[16],"focuses":[17],"on":[18,31,85,105],"a":[19,25,48,89,94],"Korteweg--de":[20],"Vries":[21],"equation,":[22],"which":[23],"is":[24,45,75,101,112],"nonlinear":[26,127],"mathematical":[27],"model":[28],"waves":[30],"shallow":[32],"water":[33],"surfaces.":[34],"Two":[35],"different":[36],"types":[37],"are":[41],"considered.":[42],"The":[43,65],"well-posedness":[44],"proven":[46],"applying":[47],"Banach":[49],"fixed-point":[50],"theorem,":[51],"using":[52],"some":[53,59],"estimates":[54],"this":[56],"equation":[57],"and":[58],"properties":[60],"saturation":[63],"function.":[64],"proof":[66],"asymptotic":[69],"stability":[70,123],"closed-loop":[73,126],"system":[74],"separated":[76],"two":[78],"cases:":[79],"(i)":[80],"when":[81,109],"control":[83,111],"acts":[84],"all":[86],"domain,":[88],"Lyapunov":[90],"function":[91],"together":[92],"sector":[95],"condition":[96],"describing":[97],"saturating":[99],"input":[100],"used":[102],"to":[103],"conclude":[104],"stability;":[107],"(ii)":[108],"localized,":[113],"we":[114],"argue":[115],"by":[116],"contradiction.":[117],"Some":[118],"numerical":[119],"simulations":[120],"illustrate":[121],"equation.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}