{"id":"https://openalex.org/W2327946538","doi":"https://doi.org/10.1137/141000415","title":"Second Order Analysis for Strong Solutions in the Optimal Control of Parabolic Equations","display_name":"Second Order Analysis for Strong Solutions in the Optimal Control of Parabolic Equations","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2327946538","doi":"https://doi.org/10.1137/141000415","mag":"2327946538"},"language":"en","primary_location":{"id":"doi:10.1137/141000415","is_oa":false,"landing_page_url":"https://doi.org/10.1137/141000415","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-01096149","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034967527","display_name":"T\u00e9rence Bayen","orcid":"https://orcid.org/0000-0002-0303-6581"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"T\u00e9rence Bayen","raw_affiliation_strings":["IMAG - Institut Montpelli\u00e9rain Alexander Grothendieck (UMR CNRS 5149 - Universit\u00e9 Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5 - France - France)"],"affiliations":[{"raw_affiliation_string":"IMAG - Institut Montpelli\u00e9rain Alexander Grothendieck (UMR CNRS 5149 - Universit\u00e9 Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5 - France - France)","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028307796","display_name":"Francisco J. Silva","orcid":"https://orcid.org/0000-0002-6911-6541"},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Francisco J. Silva","raw_affiliation_strings":["XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (XLIM -  123, avenue Albert Thomas - 87060 LIMOGES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (XLIM -  123, avenue Albert Thomas - 87060 LIMOGES CEDEX - France)","institution_ids":["https://openalex.org/I4210093397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034967527"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307"],"apc_list":null,"apc_paid":null,"fwci":3.2207,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.90651581,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"54","issue":"2","first_page":"819","last_page":"844"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7761225700378418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7751511931419373},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6937109231948853},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.651192843914032},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.4965375065803528},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4927110970020294},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4746839702129364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3918185830116272},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2631809115409851},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05980905890464783}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7761225700378418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7751511931419373},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6937109231948853},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.651192843914032},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.4965375065803528},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4927110970020294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4746839702129364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3918185830116272},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2631809115409851},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05980905890464783}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/141000415","is_oa":false,"landing_page_url":"https://doi.org/10.1137/141000415","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-01096149v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01096149","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":"SIAM Journal on Control and Optimization, 2016, 54 (2), pp.819-844. ⟨10.1137/141000415⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-01313949v1","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01313949","pdf_url":null,"source":{"id":"https://openalex.org/S4406922276","display_name":"INRIA a CCSD electronic archive server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0363-0129","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01096149v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01096149","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":"SIAM Journal on Control and Optimization, 2016, 54 (2), pp.819-844. ⟨10.1137/141000415⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W276602048","https://openalex.org/W1013854825","https://openalex.org/W1554611982","https://openalex.org/W1589236075","https://openalex.org/W1820125862","https://openalex.org/W1982312692","https://openalex.org/W1984483167","https://openalex.org/W1992510177","https://openalex.org/W1993647205","https://openalex.org/W2013354254","https://openalex.org/W2020071646","https://openalex.org/W2029123910","https://openalex.org/W2043841940","https://openalex.org/W2048164789","https://openalex.org/W2058731469","https://openalex.org/W2063819119","https://openalex.org/W2068254260","https://openalex.org/W2073078790","https://openalex.org/W2076176003","https://openalex.org/W2082751654","https://openalex.org/W2121610556","https://openalex.org/W2130595122","https://openalex.org/W2157713021","https://openalex.org/W2312382730","https://openalex.org/W2369386221","https://openalex.org/W2790417441"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W4210340977"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,43,61,100,143],"provide":[4,101],"a":[5,31,40,57,63,92,102,126],"second":[6,104],"order":[7,105],"analysis":[8],"for":[9,75,108],"strong":[10,72,153],"solutions":[11],"in":[12,30,36,56,70,95,131,151,164],"the":[13,22,28,37,50,53,66,71,85,88,96,109,118,121,132,141,146,152,157,165,178],"optimal":[14],"control":[15,29],"of":[16,24,39,65,87,120,128,148,161],"parabolic":[17],"equations.":[18],"We":[19],"consider":[20],"first":[21,54],"case":[23,38],"box":[25],"constraints":[26,48],"on":[27,49,140],"general":[32,59],"setting":[33],"and":[34],"then,":[35],"quadratic":[41,67,93,111,133,149,162],"Hamiltonian,":[42],"also":[44],"impose":[45,117],"final":[46],"integral":[47],"state.":[51],"For":[52],"problem,":[55],"rather":[58],"framework,":[60],"prove":[62,144],"characterization":[64],"growth":[68,112,150,163],"property":[69],"sense,":[73,167],"i.e.,":[74,168],"admissible":[76],"controls":[77,172],"whose":[78],"associated":[79],"states":[80],"are":[81,174],"uniformly":[82,175],"near":[83,176],"to":[84,171,177],"state":[86,97],"nominal":[89,179],"control.":[90],"Assuming":[91],"Hamiltonian":[94,134],"constrained":[98],"case,":[99,135],"sufficient":[103],"optimality":[106],"condition":[107],"aforementioned":[110],"property,":[113],"which":[114,173],"does":[115],"not":[116],"uniqueness":[119],"Lagrange":[122],"multiplier":[123],"set.":[124],"As":[125],"consequence":[127],"our":[129],"results,":[130],"under":[136],"some":[137],"continuity":[138],"assumptions":[139],"data":[142],"that":[145],"notions":[147],"sense":[154],"coincide":[155],"with":[156,169],"more":[158],"standard":[159],"notion":[160],"weak":[166],"respect":[170],"one.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}