{"id":"https://openalex.org/W2043967263","doi":"https://doi.org/10.1155/2012/389450","title":"Adaptive Stabilization of the Korteweg\u2010de Vries\u2010Burgers Equation with Unknown Dispersion","display_name":"Adaptive Stabilization of the Korteweg\u2010de Vries\u2010Burgers Equation with Unknown Dispersion","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2043967263","doi":"https://doi.org/10.1155/2012/389450","mag":"2043967263"},"language":"en","primary_location":{"id":"doi:10.1155/2012/389450","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/389450","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/389450.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/389450.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100512558","display_name":"Xiaoyan Deng","orcid":"https://orcid.org/0000-0002-5391-766X"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoyan Deng","raw_affiliation_strings":["Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, China","Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013, China","Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013","Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100345572","display_name":"Lixin Tian","orcid":"https://orcid.org/0000-0002-4550-2472"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lixin Tian","raw_affiliation_strings":["Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, China","Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013, China","Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013","Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101609834","display_name":"Wenxia Chen","orcid":"https://orcid.org/0000-0002-0503-9022"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenxia Chen","raw_affiliation_strings":["Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, China","Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013, China","Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013","Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Jiangsu, Zhenjiang 212013","institution_ids":["https://openalex.org/I115592961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100512558"],"corresponding_institution_ids":["https://openalex.org/I115592961"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10840365,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9991000294685364,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7307608723640442},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5828534960746765},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.5523779392242432},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5143495798110962},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4711766839027405},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4392138421535492},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.4332905411720276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4205547571182251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4154564440250397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21789851784706116},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1848791241645813},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.11510643362998962}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7307608723640442},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5828534960746765},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.5523779392242432},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5143495798110962},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4711766839027405},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4392138421535492},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.4332905411720276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4205547571182251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4154564440250397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21789851784706116},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1848791241645813},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.11510643362998962},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"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},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/389450","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/389450","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/389450.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1357153526","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1357153526","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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:RePEc:hin:jnljam:389450","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/389450.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:ee7444abbef14b0a910b3d4940f21e97","is_oa":true,"landing_page_url":"https://doaj.org/article/ee7444abbef14b0a910b3d4940f21e97","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/389450","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/389450","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/389450.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1463438273","display_name":null,"funder_award_id":"201032","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2578881840","display_name":null,"funder_award_id":"11171135","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4852801203","display_name":null,"funder_award_id":"71073072","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4917176502","display_name":null,"funder_award_id":"09KJB110003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7495184829","display_name":null,"funder_award_id":"BK2010329","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8371543952","display_name":null,"funder_award_id":"1171135","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2043967263.pdf","grobid_xml":"https://content.openalex.org/works/W2043967263.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1964003663","https://openalex.org/W2044497027","https://openalex.org/W2077430331","https://openalex.org/W2131785624","https://openalex.org/W2147793011","https://openalex.org/W2188832871","https://openalex.org/W2361039615","https://openalex.org/W2362964071","https://openalex.org/W7058226021"],"related_works":["https://openalex.org/W2369511497","https://openalex.org/W2319082512","https://openalex.org/W1968180156","https://openalex.org/W2351208265","https://openalex.org/W2048471423","https://openalex.org/W2368637410","https://openalex.org/W2110627003","https://openalex.org/W1519781192","https://openalex.org/W2360464268","https://openalex.org/W2471685969"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,8,13,20,24,40,43,61],"adaptive":[4],"control":[5],"problem":[6],"of":[7,42],"Korteweg\u2010de":[9],"Vries\u2010Burgers":[10],"equation.":[11],"Using":[12],"Lyapunov":[14],"function":[15],"method,":[16],"we":[17,37],"prove":[18],"that":[19,39],"closed\u2010loop":[21,65],"system":[22,44,66],"including":[23],"parameter":[25],"estimator":[26],"as":[27],"a":[28],"dynamic":[29],"component":[30],"is":[31,45,67],"globally":[32],"L":[33],"2":[34],"stable.":[35],"Furthermore,":[36],"show":[38],"state":[41],"regulated":[46],"to":[47,53,69],"zero":[48],"by":[49],"developing":[50],"an":[51],"alternative":[52],"Barbalat\u2032s":[54],"lemma":[55],"which":[56],"cannot":[57],"be":[58,70],"used":[59],"in":[60],"present":[62],"situation.":[63],"The":[64],"shown":[68],"well":[71],"posed.":[72]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
