{"id":"https://openalex.org/W4289781164","doi":"https://doi.org/10.1137/21m1434581","title":"Global Well-Posedness of the KdV Equation on a Star-Shaped Network and Stabilization by Saturated Controllers","display_name":"Global Well-Posedness of the KdV Equation on a Star-Shaped Network and Stabilization by Saturated Controllers","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4289781164","doi":"https://doi.org/10.1137/21m1434581"},"language":"en","primary_location":{"id":"doi:10.1137/21m1434581","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1434581","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-03831316","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060673452","display_name":"Hugo Parada","orcid":"https://orcid.org/0000-0003-4121-2934"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hugo Parada","raw_affiliation_strings":["EDP - Equations aux D\u00e9riv\u00e9es Partielles (France)"],"affiliations":[{"raw_affiliation_string":"EDP - Equations aux D\u00e9riv\u00e9es Partielles (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026551038","display_name":"Emmanuelle Cr\u00e9peau","orcid":"https://orcid.org/0000-0002-1149-1955"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emmanuelle Cr\u00e9peau","raw_affiliation_strings":["EDP - Equations aux D\u00e9riv\u00e9es Partielles (France)"],"affiliations":[{"raw_affiliation_string":"EDP - Equations aux D\u00e9riv\u00e9es Partielles (France)","institution_ids":[]}]},{"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/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-INFINITY - GIPSA - Infinite Dimensional Dynamics (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX  - France)"],"affiliations":[{"raw_affiliation_string":"GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX  - France)","institution_ids":["https://openalex.org/I4210124956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060673452"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9033,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94931373,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"4","first_page":"2268","last_page":"2296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9987999796867371,"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":0.9987999796867371,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9854000210762024,"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/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.7978103160858154},{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.6136868000030518},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5246025323867798},{"id":"https://openalex.org/keywords/publics","display_name":"Publics","score":0.48749279975891113},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3746298551559448},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.36875393986701965},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.35086286067962646},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.33014172315597534},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.2450602948665619},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.23634320497512817},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20812329649925232},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19305375218391418},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.15830188989639282}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.7978103160858154},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.6136868000030518},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5246025323867798},{"id":"https://openalex.org/C2776663400","wikidata":"https://www.wikidata.org/wiki/Q7258081","display_name":"Publics","level":3,"score":0.48749279975891113},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3746298551559448},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.36875393986701965},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.35086286067962646},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33014172315597534},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.2450602948665619},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.23634320497512817},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20812329649925232},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19305375218391418},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.15830188989639282},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1434581","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1434581","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-03831316v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03831316","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://epubs.siam.org/doi/10.1137/21M1434581","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03831316v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03831316","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://epubs.siam.org/doi/10.1137/21M1434581","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5}],"awards":[{"id":"https://openalex.org/G6825150759","display_name":null,"funder_award_id":"ANR-15-IDEX-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7442926511","display_name":null,"funder_award_id":"ANR-19-P3IA-0003","funder_id":"https://openalex.org/F4320313937","funder_display_name":"Universit\u00e9 Grenoble Alpes"}],"funders":[{"id":"https://openalex.org/F4320313937","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187"},{"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":28,"referenced_works":["https://openalex.org/W46317803","https://openalex.org/W653486459","https://openalex.org/W1866709725","https://openalex.org/W1967694241","https://openalex.org/W1979722387","https://openalex.org/W1980366322","https://openalex.org/W1985982935","https://openalex.org/W2024081271","https://openalex.org/W2024472896","https://openalex.org/W2066888772","https://openalex.org/W2086519672","https://openalex.org/W2091019995","https://openalex.org/W2136187884","https://openalex.org/W2262343329","https://openalex.org/W2344666630","https://openalex.org/W2502764250","https://openalex.org/W2521163219","https://openalex.org/W2554188517","https://openalex.org/W2610456553","https://openalex.org/W2890181851","https://openalex.org/W2963056581","https://openalex.org/W2966452828","https://openalex.org/W3100259381","https://openalex.org/W3102599150","https://openalex.org/W3103765657","https://openalex.org/W3106329704","https://openalex.org/W3151680498","https://openalex.org/W3170731810"],"related_works":["https://openalex.org/W2991823240","https://openalex.org/W2493872841","https://openalex.org/W3168503264","https://openalex.org/W2036535694","https://openalex.org/W2979436816","https://openalex.org/W2802661453","https://openalex.org/W4300782144","https://openalex.org/W2012209553","https://openalex.org/W3103965378","https://openalex.org/W2024710114"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,54,61],"deal":[4,55],"with":[5,26,56],"the":[6,12,31,36,41,57,63],"global":[7,32],"well-posedness":[8,33],"and":[9,14,44,49],"stability":[10,65],"of":[11,70],"linear":[13,42],"nonlinear":[15,58],"Korteweg-de":[16],"Vries":[17],"equations":[18],"on":[19],"a":[20,50,78],"finite":[21],"star-shaped":[22],"network":[23],"by":[24,34,72],"acting":[25],"saturated":[27],"controls.":[28],"We":[29],"obtain":[30,62],"using":[35,46,66],"Kato":[37],"smoothing":[38],"property":[39],"for":[40],"case":[43],"then":[45],"some":[47],"estimates":[48],"fixed":[51],"point":[52],"argument":[53],"system.":[59],"Finally,":[60],"exponential":[64],"two":[67],"different":[68],"kinds":[69],"saturation":[71],"proving":[73],"an":[74],"observability":[75],"inequality":[76],"via":[77],"contradiction":[79],"argument.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
