{"id":"https://openalex.org/W1984235937","doi":"https://doi.org/10.1137/s0363012901386465","title":"On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient","display_name":"On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1984235937","doi":"https://doi.org/10.1137/s0363012901386465","mag":"1984235937"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012901386465","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901386465","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://eprints.ucm.es/id/eprint/12178/1/2001onthecon-19.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015620652","display_name":"Anna Doubova","orcid":"https://orcid.org/0000-0002-5708-2700"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Doubova","raw_affiliation_strings":["Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089272022","display_name":"Enrique Fern\u00e1ndez\u2010Cara","orcid":"https://orcid.org/0000-0001-6293-9249"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E. Fern\u00e1ndez-Cara","raw_affiliation_strings":["Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010553301","display_name":"Manuel Gonz\u00e1lez-Burgos","orcid":"https://orcid.org/0000-0002-3012-4296"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. Gonz\u00e1lez-Burgos","raw_affiliation_strings":["Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088702266","display_name":"Enrique Zuazua","orcid":"https://orcid.org/0000-0002-1377-0958"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E. Zuazua","raw_affiliation_strings":["Dpto. Matem\u00e1tica Aplicada, Universidad Complutense, 28040 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. Matem\u00e1tica Aplicada, Universidad Complutense, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4712,"has_fulltext":false,"cited_by_count":154,"citation_normalized_percentile":{"value":0.93857395,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"41","issue":"3","first_page":"798","last_page":"819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9624999761581421,"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/mathematics","display_name":"Mathematics","score":0.8837051391601562},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.8716760873794556},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8316045999526978},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6078691482543945},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5802254676818848},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5432577729225159},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5421401858329773},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5318115949630737},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5156747102737427},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5083581805229187},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.47753989696502686},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4353184103965759},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3689599931240082},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3389776945114136},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.26135575771331787},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.12566527724266052},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06321948766708374}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8837051391601562},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.8716760873794556},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8316045999526978},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6078691482543945},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5802254676818848},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5432577729225159},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5421401858329773},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5318115949630737},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5156747102737427},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5083581805229187},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.47753989696502686},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4353184103965759},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3689599931240082},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3389776945114136},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26135575771331787},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.12566527724266052},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06321948766708374},{"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/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0363012901386465","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901386465","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:dnet:idus________::6ae05b4e45d8fe2d9a4a0602f8e9d4c6","is_oa":false,"landing_page_url":"https://idus.us.es/handle/11441/41189","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dnet:eprintscompl::07f837f6cbd051c105def1a97fae55d7","is_oa":true,"landing_page_url":"https://eprints.ucm.es/id/eprint/12178/1/2001onthecon-19.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.ucm.es:12178","is_oa":true,"landing_page_url":"https://eprints.ucm.es/12178/1/2001onthecon-19.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400298","display_name":"Library Open Repository (Universidad Complutense Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I121748325","host_organization_name":"Universidad Complutense de Madrid","host_organization_lineage":["https://openalex.org/I121748325"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dnet:eprintscompl::07f837f6cbd051c105def1a97fae55d7","is_oa":true,"landing_page_url":"https://eprints.ucm.es/id/eprint/12178/1/2001onthecon-19.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W288247418","https://openalex.org/W355022558","https://openalex.org/W630764638","https://openalex.org/W1973697519","https://openalex.org/W1986721566","https://openalex.org/W2042669370","https://openalex.org/W2051202723","https://openalex.org/W2073078790","https://openalex.org/W2087578104","https://openalex.org/W2121552308","https://openalex.org/W2252713038","https://openalex.org/W2312961750","https://openalex.org/W2369386221","https://openalex.org/W2497745768","https://openalex.org/W4244196985"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W2036697162","https://openalex.org/W2332386680","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W2316191048","https://openalex.org/W4389471227","https://openalex.org/W1569734721","https://openalex.org/W3010940295","https://openalex.org/W4383473391"],"abstract_inverted_index":{"We":[0,27,52],"present":[1],"some":[2],"results":[3],"concerning":[4],"the":[5,29,50,55,66,97,112],"controllability":[6,30],"of":[7,20,49,99],"a":[8,17,37,46],"quasi-linear":[9],"parabolic":[10,109],"equation":[11],"(with":[12],"linear":[13],"principal":[14],"part)":[15],"in":[16,93,96],"bounded":[18],"domain":[19],"${\\mathbb":[21],"R}^N$":[22],"with":[23,32],"Dirichlet":[24],"boundary":[25,42],"conditions.":[26],"analyze":[28],"problem":[31],"distributed":[33],"controls":[34,43],"(supported":[35,44],"on":[36,45],"small":[38,47],"open":[39],"subset)":[40],"and":[41,59,111],"part":[48],"boundary).":[51],"prove":[53],"that":[54],"system":[56],"is":[57],"null":[58],"approximately":[60],"controllable":[61],"at":[62,90],"any":[63],"time":[64],"if":[65],"nonlinear":[67],"term":[68],"$f(":[69],"y,":[70],"\\nabla":[71],"y)$":[72],"grows":[73],"slower":[74],"than":[75],"$|y|":[76],"\\log^{3/2}(1+":[77],"|y|":[78,86],"+":[79,82,87],"|\\nabla":[80,83,88],"y|)":[81],"y|":[84],"\\log^{1/2}(1+":[85],"y|)$":[89],"infinity":[91],"(generally,":[92],"this":[94],"case,":[95],"absence":[98],"control,":[100],"blow-up":[101],"occurs).":[102],"The":[103],"proofs":[104],"use":[105],"global":[106],"Carleman":[107],"estimates,":[108],"regularity,":[110],"fixed":[113],"point":[114],"method.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":7}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
