{"id":"https://openalex.org/W3018817671","doi":"https://doi.org/10.1137/19m1240472","title":"Controllability and Stabilizability of a Higher Order Wave Equation on a Periodic Domain","display_name":"Controllability and Stabilizability of a Higher Order Wave Equation on a Periodic Domain","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3018817671","doi":"https://doi.org/10.1137/19m1240472","mag":"3018817671"},"language":"en","primary_location":{"id":"doi:10.1137/19m1240472","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1240472","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/A5101953090","display_name":"Shenghao Li","orcid":"https://orcid.org/0000-0001-5842-2212"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shenghao Li","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5842-2212","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100337209","display_name":"Min Chen","orcid":"https://orcid.org/0000-0002-0960-4447"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Min Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100720753","display_name":"Bing\u2010Yu Zhang","orcid":"https://orcid.org/0000-0001-9057-7257"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bingyu Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5283,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7959863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"2","first_page":"1121","last_page":"1143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9926000237464905,"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/T13234","display_name":"advanced mathematical theories","score":0.9002000093460083,"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/controllability","display_name":"Controllability","score":0.8820039629936218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8099300265312195},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.7303512692451477},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6679495573043823},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6142841577529907},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5538983941078186},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.485493928194046},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4528076648712158},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36883544921875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35521990060806274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.11767905950546265}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8820039629936218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8099300265312195},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.7303512692451477},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6679495573043823},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6142841577529907},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5538983941078186},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.485493928194046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4528076648712158},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36883544921875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35521990060806274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.11767905950546265},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1240472","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1240472","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1966154362","https://openalex.org/W1971071908","https://openalex.org/W1971888625","https://openalex.org/W1980351744","https://openalex.org/W1989537265","https://openalex.org/W2001304956","https://openalex.org/W2011527288","https://openalex.org/W2030248932","https://openalex.org/W2046741348","https://openalex.org/W2079600388","https://openalex.org/W2081416224","https://openalex.org/W2086519672","https://openalex.org/W2091019995","https://openalex.org/W2098750612","https://openalex.org/W2101694485","https://openalex.org/W2128039433","https://openalex.org/W2130921294","https://openalex.org/W2140953416","https://openalex.org/W2328944148","https://openalex.org/W2794063837","https://openalex.org/W2897516046","https://openalex.org/W2963869019"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2332386680","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W2038998384","https://openalex.org/W2534004512","https://openalex.org/W4225370548","https://openalex.org/W1980471957","https://openalex.org/W2080798677","https://openalex.org/W279919757"],"abstract_inverted_index":{"This":[0],"article":[1],"studies":[2],"internal":[3,22],"control":[4,23],"of":[5,33],"the":[6,21,34,41,51],"sixth":[7],"order":[8],"Boussinesq":[9],"equation":[10],"$u_{tt}-u_{xx}+\\beta":[11],"u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f":[12],"$":[13],"posed":[14],"on":[15,27],"a":[16],"periodic":[17],"domain":[18,35],"$\\mathbb{T}$":[19],"with":[20],"input":[24],"$f(\\cdot,t)$":[25],"acting":[26],"an":[28],"arbitrarily":[29],"small":[30],"open":[31],"subset":[32],"$\\mathbb{T}$.":[36],"It":[37],"is":[38,43],"shown":[39],"that":[40],"system":[42],"locally":[44],"exactly":[45],"controllable":[46],"and":[47],"exponentially":[48],"stabilizable":[49],"in":[50],"classic":[52],"Sobolev":[53],"space":[54],"$H^{s+3}(\\mathbb{T})\\times":[55],"H^s(\\mathbb{T})$":[56],"for":[57],"any":[58],"$s\\geq":[59],"0$.":[60]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}