{"id":"https://openalex.org/W2038021629","doi":"https://doi.org/10.1137/s0363012902419011","title":"On the Bellman Equation for the Minimum Time Problem in Infinite Dimensions","display_name":"On the Bellman Equation for the Minimum Time Problem in Infinite Dimensions","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2038021629","doi":"https://doi.org/10.1137/s0363012902419011","mag":"2038021629"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012902419011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902419011","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/A5049253329","display_name":"Piermarco Cannarsa","orcid":"https://orcid.org/0000-0003-2576-2004"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piermarco Cannarsa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032979048","display_name":"Ovidiu Carj\u00f9a","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ovidiu C\u00e2rjua","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":6.1006,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.95366299,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"43","issue":"2","first_page":"532","last_page":"548"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9900000095367432,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9024450778961182},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6742555499076843},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.6704732179641724},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6395571231842041},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6209244728088379},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.563453733921051},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.5628045201301575},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5209506750106812},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5073754191398621},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37337368726730347},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25306758284568787}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9024450778961182},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6742555499076843},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.6704732179641724},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6395571231842041},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6209244728088379},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.563453733921051},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.5628045201301575},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5209506750106812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5073754191398621},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37337368726730347},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25306758284568787},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012902419011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902419011","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1487586009","https://openalex.org/W1496662771","https://openalex.org/W1528796636","https://openalex.org/W1960239420","https://openalex.org/W1971519255","https://openalex.org/W1978169712","https://openalex.org/W1979308690","https://openalex.org/W1984213605","https://openalex.org/W2016565920","https://openalex.org/W2029311671","https://openalex.org/W2029313357","https://openalex.org/W2037048586","https://openalex.org/W2040800769","https://openalex.org/W2065296123","https://openalex.org/W2103284380","https://openalex.org/W2148316915"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W2766998270","https://openalex.org/W4255265352","https://openalex.org/W3168988147","https://openalex.org/W4239477580"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,14,17,35,41,56,62,67],"time":[3],"optimal":[4],"control":[5,11],"problem":[6],"for":[7,55],"a":[8,27],"semilinear":[9],"parabolic":[10],"system,":[12],"where":[13],"target":[15],"is":[16,65],"closed":[18],"ball":[19],"with":[20],"center":[21],"0":[22],"and":[23,52],"radius":[24],"$Rgeq0$":[25],"in":[26],"Hilbert":[28],"space":[29],"X.":[30],"In":[31],"particular,":[32],"we":[33,48],"allow":[34],"origin":[36],"of":[37],"X":[38],"to":[39],"be":[40],"target.":[42],"Using":[43],"an":[44,50],"appropriate":[45],"Kruzkov-type":[46],"transformation,":[47],"give":[49],"existence":[51],"uniqueness":[53],"result":[54],"associated":[57],"Hamilton--Jacobi--Bellman":[58],"equation,":[59],"even":[60],"when":[61],"reachable":[63],"set":[64],"not":[66],"whole":[68],"space.":[69]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
